搜索结果：Journal of molecular modeling

Previous article Next article On the Construction and Comparison of Difference SchemesGilbert StrangGilbert Stranghttps://doi.org/10.1137/0705041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Barkley Rosser, A Runge-Kutta for all seasons, SIAM Rev., 9 (1967), 417–452 10.1137/1009069 MR0219242 0243.65041 LinkISIGoogle Scholar[2] Robert D. Richtmyer and , K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967xiv+405 MR0220455 0155.47502 Google Scholar[3] Peter D. Lax and , Burton Wendroff, Difference schemes for hyperbolic equations with high order of accuracy, Comm. Pure Appl. Math., 17 (1964), 381–398 MR0170484 0233.65050 CrossrefISIGoogle Scholar[4] Samuel Z. Burstein, Numerical methods in multidimensional shocked flows, AIAA J., 2 (1964), 2111–2117 MR0180067 CrossrefGoogle Scholar[5] S. Z. Burstein, Finite-difference calculations for hydrodynamic flows containing discontinuities, J. Comp. Phys., 2 (1967), 198–222 0166.22103 Google Scholar[6] C. Berger, On the numerical range of powers of an operator, to appear Google Scholar[7] W. P. Crowley, Second-order numerical advection, J. Comp. Phys., 1 (1967), 471–484 10.1016/0021-9991(67)90053-8 0149.44403 CrossrefGoogle Scholar[8] Gilbert Strang, Accurate partial difference methods. I. Linear Cauchy problems, Arch. Rational Mech. Anal., 12 (1963), 392–402 MR0146970 0113.32303 CrossrefISIGoogle Scholar[9] A. R. Gourlay and , J. Ll. Morris, A multistep formulation of the optimized Lax-Wendroff method for nonlinear hyperbolic systems in two space variables, Math. Comp., 22 (1968), 715–719 MR0251931 0172.19904 CrossrefISIGoogle Scholar[10] Peter Lax and , Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math., 13 (1960), 217–237 MR0120774 0152.44802 CrossrefISIGoogle Scholar[11] R. D. Richtmyer, A survey of difference methods for nonsteady fluid dynamics, Tech. Note, 63-2, National Center for Atmospheric Research, Boulder, Colorado, 1962 Google Scholar[12] Gilbert Strang, Accurate partial difference methods. II. Non-linear problems, Numer. Math., 6 (1964), 37–46 10.1007/BF01386051 MR0166942 0143.38204 CrossrefGoogle Scholar[13] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407 MR0135729 0112.34901 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Semiexplicit symplectic integrators for non-separable Hamiltonian systems23 September 2022 | Mathematics of Computation, Vol. 92, No. 339 Cross Ref A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemesJournal of Computational Physics, Vol. 472 Cross Ref Numerical computation for rogue waves in the coupled nonlinear Schrödinger equations with the coherent coupling effect29 April 2022 | International Journal of Computer Mathematics, Vol. 99, No. 12 Cross Ref A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systemsMathematics and Computers in Simulation, Vol. 202 Cross Ref Ultrafast laser matter interactions: modeling approaches, challenges, and prospects27 September 2022 | Modelling and Simulation in Materials Science and Engineering, Vol. 30, No. 8 Cross Ref An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gasesJournal of Computational Physics, Vol. 471 Cross Ref Implications of CO 2 mass transport dynamics for large-scale CCS in basalt formationsInternational Journal of Greenhouse Gas Control, Vol. 121 Cross Ref A charge-preserving compact splitting method for solving the coupled stochastic nonlinear Schrödinger equationsApplied Numerical Mathematics, Vol. 181 Cross Ref Local effects in vortex-flame interactions: Implications for turbulent premixed flame scaling and observablesCombustion and Flame, Vol. 245 Cross Ref Hamiltonian preserving nonlinear opticsPhysica D: Nonlinear Phenomena, Vol. 439 Cross Ref A fully coupled, fully implicit simulation method for unsteady flames using Jacobian approximation and clusteringCombustion and Flame, Vol. 245 Cross Ref Reactive Transport Modeling with a Coupled OpenFOAM®-PHREEQC Platform7 October 2022 | Transport in Porous Media, Vol. 145, No. 2 Cross Ref Multirate Exponential Rosenbrock MethodsVu Thai Luan, Rujeko Chinomona, and Daniel R. Reynolds13 October 2022 | SIAM Journal on Scientific Computing, Vol. 44, No. 5AbstractPDF (764 KB)Assessment of a new sub-grid model for magnetohydrodynamical turbulence. I. Magnetorotational instability10 October 2022 | Monthly Notices of the Royal Astronomical Society, Vol. 517, No. 3 Cross Ref Consistent submodel coupling in hybrid particle/finite volume algorithms for zone-adaptive modelling of turbulent reactive flows12 October 2022 | Combustion Theory and Modelling, Vol. 1 Cross Ref Real-time propagator eigenstates2 September 2022 | Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 55, No. 19 Cross Ref Operator splitting scheme based on barycentric Lagrange interpolation collocation method for the Allen-Cahn equation19 November 2021 | Journal of Applied Mathematics and Computing, Vol. 68, No. 5 Cross Ref Dynamics of Electron Pearcey– Gaussian Beams in a Constant Magnetic Field5 August 2022 | Annalen der Physik, Vol. 534, No. 10 Cross Ref Synergistic interactions of thermodiffusive instabilities and turbulence in lean hydrogen flamesCombustion and Flame, Vol. 244 Cross Ref General time-dependent configuration-interaction singles. II. Atomic case10 October 2022 | Physical Review A, Vol. 106, No. 4 Cross Ref A high order accurate numerical algorithm for the space-fractional Swift-Hohenberg equationComputers & Mathematics with Applications, Vol. 15 Cross Ref A self-adaptive theta scheme using discontinuity aware quadrature for solving conservation laws19 October 2021 | IMA Journal of Numerical Analysis, Vol. 42, No. 4 Cross Ref Isolating gasdynamic and chemical effects on the detonation cellular structure: A combined experimental and computational studyProceedings of the Combustion Institute, Vol. 9 Cross Ref Improved Uniform Error Bounds on Time-Splitting Methods for the Long-Time Dynamics of the Dirac Equation with Small Potentials Weizhu Bao , Yue Feng , and Jia Yin 27 September 2022 | Multiscale Modeling & Simulation, Vol. 20, No. 3AbstractPDF (16068 KB)Improving the Performance of Reactive Transport Simulations Using Artificial Neural Networks27 September 2022 | Transport in Porous Media, Vol. 513 Cross Ref Signatures of coherent vibronic exciton dynamics and conformational control in the two-dimensional electronic spectroscopy of conjugated polymers1 January 2022 | Faraday Discussions, Vol. 237 Cross Ref Robust estimation of charge carrier diffusivity using transient photoluminescence microscopyThe Journal of Chemical Physics, Vol. 157, No. 10 Cross Ref Electron Symmetric Pearcey Gaussian Vortex Beams5 August 2022 | Annalen der Physik, Vol. 534, No. 9 Cross Ref An enhanced semi-explicit particle finite element method for incompressible flows30 May 2022 | Computational Mechanics, Vol. 70, No. 3 Cross Ref A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo modelApplied Numerical Mathematics, Vol. 179 Cross Ref Far-field sonic boom prediction considering atmospheric turbulence effects: An improved approachChinese Journal of Aeronautics, Vol. 35, No. 9 Cross Ref An Improved Method for Coupling Hydrodynamics with Astrophysical Reaction Networks25 August 2022 | The Astrophysical Journal, Vol. 936, No. 1 Cross Ref High-order interpolatory Serendipity Virtual Element Method for semilinear parabolic problems14 June 2022 | Calcolo, Vol. 59, No. 3 Cross Ref Effects of wedge-angle change on the evolution of oblique detonation wave structurePhysics of Fluids, Vol. 34, No. 9 Cross Ref HPC-enabling technologies for high-fidelity combustion simulationsProceedings of the Combustion Institute, Vol. 33 Cross Ref A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational FormulationChun Liu, Cheng Wang, and Yiwei Wang2 August 2022 | SIAM Journal on Scientific Computing, Vol. 44, No. 4AbstractPDF (1148 KB)Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak NonlinearityWeizhu Bao, Yongyong Cai, and Yue Feng1 August 2022 | SIAM Journal on Numerical Analysis, Vol. 60, No. 4AbstractPDF (41582 KB)Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamics11 August 2022 | BIT Numerical Mathematics, Vol. 48 Cross Ref An effective operator splitting scheme for two-dimensional conservative nonlocal Allen–Cahn equationApplied Mathematics Letters, Vol. 130 Cross Ref A new accelerating technique for low speed flow: pseudo high speed methodChinese Journal of Aeronautics, Vol. 35, No. 8 Cross Ref The hydrodynamics of LERNAJournal of Computational Physics, Vol. 463 Cross Ref An asymptotic Green's function method for time-dependent Schrödinger equations with application to Kohn-Sham equationsJournal of Computational Physics, Vol. 463 Cross Ref Effects of differential diffusion on hydrogen flame kernel development under engine conditionsProceedings of the Combustion Institute, Vol. 14 Cross Ref Instability seeding mechanisms due to internal defects in inertial confinement fusion targetsPhysics of Plasmas, Vol. 29, No. 8 Cross Ref Investigation of droplet grouping in monodisperse streams by direct numerical simulationsPhysics of Fluids, Vol. 34, No. 8 Cross Ref The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven HohlraumsPhysics of Plasmas, Vol. 29, No. 8 Cross Ref Exponential Bhatnagar-Gross-Krook integrator for multiscale particle-based kinetic simulations4 August 2022 | Physical Review E, Vol. 106, No. 2 Cross Ref Casimir preserving spectrum of two-dimensional turbulence24 August 2022 | Physical Review Fluids, Vol. 7, No. 8 Cross Ref Learning PDE to Model Self-Organization of Matter9 August 2022 | Entropy, Vol. 24, No. 8 Cross Ref Numerical Estimation of Nozzle Throat Heat Flux in Oxygen-Methane Rocket Engines18 July 2022 | Journal of Propulsion and Power, Vol. 87 Cross Ref A sixth order entropy condition scheme for compressible flowComputers & Fluids, Vol. 243 Cross Ref Explore artificial neural networks for solving complex hydrocarbon chemistry in turbulent reactive flowsFundamental Research, Vol. 2, No. 4 Cross Ref High-order Scharfetter-Gummel-based schemes and applications to gas discharge modelingJournal of Computational Physics, Vol. 461 Cross Ref Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equationMathematics and Computers in Simulation, Vol. 197 Cross Ref Graphite Nozzle Erosion Trends in Paraffin/Oxygen Hybrid RocketsJournal of Propulsion and Power, Vol. 38, No. 4 Cross Ref A Massively Parallel Eulerian-Lagrangian Method for Advection-Dominated Transport in Viscous FluidsNils Kohl, Marcus Mohr, Sebastian Eibl, and Ulrich Rüde24 June 2022 | SIAM Journal on Scientific Computing, Vol. 44, No. 3AbstractPDF (52728 KB)Modeling of Wall Heat Flux in Oxygen-Methane Liquid Rocket Thrust Chambers20 June 2022 Cross Ref Verification and Validation of Immersed Boundary Solvers for Hypersonic Flows with Gas-Surface Interactions20 June 2022 Cross Ref Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump23 February 2022 | International Journal for Numerical Methods in Fluids, Vol. 94, No. 6 Cross Ref Second-order maximum principle preserving Strang’s splitting schemes for anisotropic fractional Allen-Cahn equations30 September 2021 | Numerical Algorithms, Vol. 90, No. 2 Cross Ref Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. Part 1 - Dispersion relations in the linear regimeCombustion and Flame, Vol. 240 Cross Ref Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn equationJournal of Computational Physics, Vol. 458 Cross Ref A dynamic relaxation method with operator splitting and random-choice strategy for SPHJournal of Computational Physics, Vol. 458 Cross Ref Numerical prediction of loudness metrics for N-waves and shaped sonic booms in kinematic turbulenceThe Journal of the Acoustical Society of America, Vol. 151, No. 6 Cross Ref Magneto-thermal instability in galaxy clusters – I. Theory and two-dimensional simulations9 April 2022 | Monthly Notices of the Royal Astronomical Society, Vol. 513, No. 3 Cross Ref Computational Fluid Dynamics of Reacting Flows at Surfaces: Methodologies and Applications26 February 2022 | Chemie Ingenieur Technik, Vol. 94, No. 5 Cross Ref Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motionJournal of Computational and Applied Mathematics, Vol. 406 Cross Ref An improved finite integration method for nonlocal nonlinear Schrödinger equationsComputers & Mathematics with Applications, Vol. 113 Cross Ref Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithmComputer Physics Communications, Vol. 274 Cross Ref A high-order unified stochastic particle method based on the Bhatnagar-Gross-Krook model for multi-scale gas flowsComputer Physics Communications, Vol. 274 Cross Ref A new stabilised scheme for the Richards’ equation with evapotranspirationGroundwater for Sustainable Development, Vol. 17 Cross Ref Well-balanced discrete unified gas-kinetic scheme for two-phase systemsPhysics of Fluids, Vol. 34, No. 5 Cross Ref On the Physical Nature of “Anomalous” High Energy Electrons in Vacuum Diodes24 June 2022 | Russian Physics Journal, Vol. 64, No. 12 Cross Ref Stability and convergence of Strang splitting. Part II: Tensorial Allen-Cahn equationsJournal of Computational Physics, Vol. 454 Cross Ref A Model for Characteristic X-Ray Emission in Electron Probe Microanalysis Based on the (Filtered) Spherical Harmonic () Method for Electron Transport11 April 2022 | Microscopy and Microanalysis, Vol. 28, No. 2 Cross Ref Restoring the conservativity of characteristic-based segregated models: Application to the hybrid lattice Boltzmann methodPhysics of Fluids, Vol. 34, No. 4 Cross Ref An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system8 March 2022 | Journal of Plasma Physics, Vol. 88, No. 2 Cross Ref Atomistic simulation of ultra-short pulsed laser ablation of Al: an extension for non-thermalized electrons and ballistic transport29 December 2021 | Journal of Physics D: Applied Physics, Vol. 55, No. 13 Cross Ref Enhancing the Quantum Linear Systems Algorithm Using Richardson ExtrapolationACM Transactions on Quantum Computing, Vol. 3, No. 1 Cross Ref Reacting condensed phase explosives in direct contactJournal of Applied Physics, Vol. 131, No. 9 Cross Ref On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEs11 February 2022 | Journal of Scientific Computing, Vol. 90, No. 3 Cross Ref A three-dimensional Laguerre one-way wave equation solverApplied Numerical Mathematics, Vol. 173 Cross Ref Higher Order Auxiliary Field Quantum Monte Carlo MethodsJournal of Physics: Conference Series, Vol. 2207, No. 1 Cross Ref Numerical method for modeling photosynthesis of algae on pulsing soft corals31 March 2022 | Physical Review Fluids, Vol. 7, No. 3 Cross Ref Numerical Method for Approximate Solution of Fisher's Equation1 March 2022 | Journal of the Institute of Science and Technology Cross Ref Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber1 March 2022 | Fibers, Vol. 10, No. 3 Cross Ref CFD modeling of multiphase flows with detailed microkinetic description of the surface reactivityChemical Engineering Research and Design, Vol. 179 Cross Ref Nonlinear fourth order Taylor expansion of lattice Boltzmann schemesAsymptotic Analysis, Vol. 127, No. 4 Cross Ref Numerical scheme for solving a porous Saint-Venant type model for water flow on vegetated hillslopesApplied Numerical Mathematics, Vol. 172 Cross Ref A weak approximation method for irregular functionals of hypoelliptic diffusionsApplied Numerical Mathematics, Vol. 172 Cross Ref On pattern formation in reaction–diffusion systems containing self- and cross-diffusionCommunications in Nonlinear Science and Numerical Simulation, Vol. 105 Cross Ref Comparison of high-order Eulerian methods for electron hybrid modelJournal of Computational Physics, Vol. 451 Cross Ref Simulation of three-dimensional forced compressible isotropic turbulence by a redesigned discrete unified gas kinetic schemePhysics of Fluids, Vol. 34, No. 2 Cross Ref A coupled Lagrangian-Eulerian model for microplastics as vectors of contaminants applied to the Mediterranean Sea14 February 2022 | Environmental Research Letters, Vol. 17, No. 2 Cross Ref A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses22 December 2021 | Plasma Science and Technology, Vol. 24, No. 2 Cross Ref Burgers equation and convexification method: Propagation of wave packets and narrowband noiseThe Journal of the Acoustical Society of America, Vol. 151, No. 2 Cross Ref A Robust Reacting Flow Solver with Computational Diagnostics Based on OpenFOAM and Cantera14 February 2022 | Aerospace, Vol. 9, No. 2 Cross Ref Development of a Discontinuous Galerkin Ionosphere‐Plasmasphere Model3 February 2022 | Journal of Geophysical Research: Space Physics, Vol. 127, No. 2 Cross Ref Accurate and efficient simulations of Hamiltonian mechanical systems with discontinuous potentialsJournal of Computational Physics, Vol. 450 Cross Ref Stellar evolution and tidal dissipation in REBOUNDx10 January 2022 | Monthly Notices of the Royal Astronomical Society, Vol. 510, No. 4 Cross Ref Mechanisms for severe combustion instabilities induced by low-temperature fuel injection of an H 2 /O 2 rocket-type combustor29 December 2022 Cross Ref New Trends on Multiphase Flow Simulations Using Slug Capturing Approach2 April 2022 Cross Ref Modelling and Numerical Simulation of Binary Droplet Collisions Under Extreme Conditions31 August 2022 Cross Ref Investigation of the Behaviour of Supercooled Droplets Concerning Evaporation, Sublimation and Freezing Under Different Boundary Conditions31 August 2022 Cross Ref Symmetric Splitting Methods for Wave Equations: First Approaches24 September 2021 Cross Ref Efficient Experimental and Numerical Methods for Solving Vertical Distribution of Sediments in Dam-Break Flows19 May 2022 Cross Ref Aerosol–climate modeling Cross Ref Flame edge dynamics in counterflow nonpremixed flames of CH4/He versus air at low strain rates: An experimental and numerical studyCombustion and Flame, Vol. 235 Cross Ref Numerical modelling of turbulent geophysical flows using a hyperbolic shear shallow water model: Application to powder snow avalanchesComputers & Fluids, Vol. 233 Cross Ref Stochastic population balance methods for detailed modelling of flame-made aerosol particlesJournal of Aerosol Science, Vol. 159 Cross Ref Immersed boundary method for high-order flux reconstruction based on volume penalizationJournal of Computational Physics, Vol. 448 Cross Ref A unified formulation of splitting-based implicit time integration schemesJournal of Computational Physics, Vol. 448 Cross Ref Face-based in of Computational Physics, Vol. Cross Ref A hybrid method for problems with boundary in of Computational Physics, Vol. Cross Ref A computational for of of in the Vol. Cross Ref A discontinuous Galerkin in for and Vol. 17 Cross Ref Modeling of CO 2 in Reactive A January 2022 | Research, Vol. No. 1 Cross Ref for numerical simulation of January 2022 | Institute No. Cross Ref to Schemes for and January 2022 | Vol. No. 1 Cross Ref of discrete and Systems - Vol. No. 10 Cross Ref February 2022 | Vol. 5 Cross Ref numerical schemes for Hamiltonian dynamics Cross Ref Numerical Simulations on Nonlinear Quantum with the April 2022 | The Journal of computational Vol. 8 Cross Ref April 2022 Cross Ref of nonlocal and Systems - Vol. No. Cross Ref Local boundary for nonlinear Schrödinger equation with wave operator on August 2021 | Methods in the Applied Vol. 44, No. Cross Ref methods for in October 2021 | International Journal for Numerical and Methods in Vol. No. Cross Ref modeling of by a of change and December 2021 | Journal of Vol. No. Cross Ref Operator splitting and in Mathematics and Computation, Vol. Cross Ref of flow and equivalence on oblique detonation Science and Technology, Vol. Cross Ref combustion of droplet under and Flame, Vol. Cross Ref A high order operator splitting method based on for the nonlocal equationJournal of Computational Physics, Vol. Cross Ref reconstruction and schemes for volume of fluid method in of Computational Physics, Vol. Cross Ref A solver based on method for the February 2021 | Scientific Vol. No. 1 Cross Ref of of Schrödinger June 2021 | Scientific Vol. No. 1 Cross Ref and formation droplet a September 2021 | Scientific Vol. No. 1 Cross Ref of and on October 2021 | Scientific Vol. No. 1 Cross Ref Wave in of in MHD December 2021 | The Astrophysical Journal, Vol. No. 2 Cross Ref splitting methods with Journal of Chemical Physics, Vol. No. Cross Ref for simulations with Modelling & Vol. Cross Ref and Schrödinger equation with of Computational Physics, Vol. Cross Ref semilinear and the of Analysis, Vol. No. 10 Cross Ref A Numerical of Coupling Schemes for Atmospheric November 2021 | Journal of in Modeling Vol. No. Cross Ref Boundary variation conservative method for compressible and incompressible of Fluids, Vol. No. Cross Ref of Schemes in the of Vortex December 2021 | Computational Mathematics and Physics, Vol. No. Cross Ref method for the of and equations in September 2021 | Journal of Vol. No. 6 Cross Ref Conservative Schemes for Nonlinear Schrödinger Equations in a with of October 2021 | Mathematics, Vol. 9, No. Cross Ref in reactive August 2021 | Vol. No. Cross Ref Hamiltonian based approach for time in May 2021 | Molecular Physics, Vol. No. Cross Ref for Conservative Schemes for the of Nonlinear Pulse with a October 2021 | Nonlinear in Vol. 24, No. 3 Cross Ref Numerical and the for August 2021 | Journal of the Royal Society, Vol. No. Cross Ref A fully coupled two-dimensional model in August 2021 | Environmental Fluid Mechanics, Vol. No. 5 Cross Ref The formation and development of oblique detonation wave with different chemical Science and Technology, Vol. Cross Ref A improved numerical method for the simulation of rogue waves of nonlinear Schrödinger in Nonlinear Science and Numerical Simulation, Vol. Cross Ref Heat by in turbulent boundary at Journal of Heat and Vol. Cross Ref A Lagrangian-Eulerian method for of Computational Physics, Vol. Cross Ref in linear and nonlinear January 2021 | Journal of Applied Mathematics, Vol. No. 5 Cross Ref High-order geometric integrators for Journal of Chemical Physics, Vol. No. 12 Cross Ref of Flow in Gas with by Electron Cross Ref chemistry for and using flow of Applied Physics, Vol. No. Cross Ref modelling of premixed May 2021 | Combustion Theory and Modelling, Vol. No. 6 Cross Ref A numerical of control August 2021 | Vol. No. 1 Cross Ref A Conservative Semi-Lagrangian Transport Model on the July 2021 | in Atmospheric Vol. 38, No. 9 Cross Ref A Second-Order Method for Schrödinger Equations with July 2021 | Journal of Scientific Computing, Vol. 88, No. 3 Cross Ref Strang technique for the August 2021 | Vol. No. 3 Cross Ref splitting method for space-fractional Schrödinger equationApplied Numerical Mathematics, Vol. Cross Ref Numerical simulation of in the of Journal of Multiphase Vol. Cross Ref approximation of and numerical October 2021 | in Applied Vol. No. 3 Cross Ref electron dynamics in high Accurate prediction of September 2021 | Physical Review Vol. No. 10 Cross Ref On the of by the hydrogen in July 2021 | Monthly Notices of the Royal Astronomical Society, Vol. No. 2 Cross Ref Reaction Effects on Nozzle Erosion in Paraffin/Oxygen Hybrid July 2021 Cross Ref modeling in July 2021 Cross Ref A fast and efficient numerical algorithm for equation with a nonlocal Mathematics Letters, Vol. Cross Ref An particle hydrodynamics method for modeling Methods in Applied and Engineering, Vol. Cross Ref A model for droplet Journal of Heat and Vol. Cross Ref Numerical for high frequency equation efficient time for Schrödinger equationJournal of Computational Physics, Vol. Cross Ref and for and simulation of Magnetic Vol. Cross Ref Local wave

Previous article Next article Non-Parametric Estimation of a Multivariate Probability DensityV. A. EpanechnikovV. A. Epanechnikovhttps://doi.org/10.1137/1114019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Emanuel Parzen, On estimation of a probability density function and mode, Ann. Math. Statist., 33 (1962), 1065–1076 MR0143282 0116.11302 CrossrefGoogle Scholar[2] Murray Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist., 27 (1956), 832–837 MR0079873 0073.14602 CrossrefGoogle Scholar[3] G. M. Manija, Remarks on non-parametric estimates of a two-dimensional density function, Soobšč. Akad. Nauk Gruzin. SSR, 27 (1961), 385–390 MR0143303 Google Scholar[4] E. A. Nadaraya, Estimation of a bivariate probability density, Soobshch. Akad. Nauk Gruz. SSR, 36 (1964), 267–268 Google Scholar[5] R. E. Bellman, , I. Glicksberg and , O. A. Gross, Some aspects of the mathematical theory of control processes, Rand Corporation, Santa Monica, Calif., Rep. No. R-313, 1958rm xix+244 MR0094281 0086.11703 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Kernel-based learning of birth process from evolving spatiotemporal RFS data stream in SMC CPHD filter for multi-target trackingSignal Processing, Vol. 203 Cross Ref Assessing spatial connectivity effects on daily streamflow forecasting using Bayesian-based graph neural networkScience of The Total Environment, Vol. 855 Cross Ref Joint Source-Channel Decoding of Polar Codes for HEVC-Based Video StreamingACM Transactions on Multimedia Computing, Communications, and Applications, Vol. 18, No. 4 Cross Ref A novel structure adaptive new information priority discrete grey prediction model and its application in renewable energy generation forecastingApplied Energy, Vol. 325 Cross Ref A novel structure adaptive fractional discrete grey forecasting model and its application in China’s crude oil production predictionExpert Systems with Applications, Vol. 207 Cross Ref Age-varying effects of repeated emergency department presentations for children in Canada6 May 2022 | Journal of Health Services Research & Policy, Vol. 27, No. 4 Cross Ref Probabilistic adaptive power pinch analysis for islanded hybrid energy storage systemsJournal of Energy Storage, Vol. 54 Cross Ref Should I stay or should I fly? Migration phenology, individual-based migration decision and seasonal changes in foraging behaviour of Common Woodpigeons17 August 2022 | The Science of Nature, Vol. 109, No. 5 Cross Ref Machine learning and optimization based decision-support tool for seed variety selection24 September 2022 | Annals of Operations Research, Vol. 65 Cross Ref Estimating regional income indicators under transformations and access to limited population auxiliary information16 September 2022 | Journal of the Royal Statistical Society: Series A (Statistics in Society), Vol. 37 Cross Ref Automated calibration of model-driven reconstructions in atom probe tomography1 July 2022 | Journal of Physics D: Applied Physics, Vol. 55, No. 37 Cross Ref Point and interval forecasting of ultra-short-term wind power based on a data-driven method and hybrid deep learning modelEnergy, Vol. 254 Cross Ref Deep attention ConvLSTM-based adaptive fusion of clear-sky physical prior knowledge and multivariable historical information for probabilistic prediction of photovoltaic powerExpert Systems with Applications, Vol. 202 Cross Ref The Taxonomy of Mineral Occurrence Rarity and Endemicity21 October 2022 | The Canadian Mineralogist, Vol. 60, No. 5 Cross Ref Estimation of wind speed distribution with time window and new kernel functionJournal of Renewable and Sustainable Energy, Vol. 14, No. 5 Cross Ref Future crop risk estimation due to drought, extreme temperature, hail, lightning, and tornado at the census tract level in louisiana23 August 2022 | Frontiers in Environmental Science, Vol. 10 Cross Ref Translocation detection from Hi‐C data via scan statistics10 August 2022 | Biometrics, Vol. 8 Cross Ref Does restricting therapeutic antibiotics use influence efficiency of pig farms? Evidence from Denmark’s Yellow Card Initiative18 May 2022 | European Review of Agricultural Economics, Vol. 49, No. 4 Cross Ref Computational approach to modeling microbiome landscapes associated with chronic human disease progression4 August 2022 | PLOS Computational Biology, Vol. 18, No. 8 Cross Ref Spillovers between exchange rate pressure and CDS bid-ask spreads, reserve assets and oil prices using the quantile ARDL modelInternational Economics, Vol. 170 Cross Ref Liability Structure and Risk Taking: Evidence from the Money Market Fund Industry18 June 2021 | Journal of Financial and Quantitative Analysis, Vol. 57, No. 5 Cross Ref Security risk assessment of wind integrated power system using Parzen window density estimation6 January 2022 | Electrical Engineering, Vol. 104, No. 4 Cross Ref Predator or prey? Effects of farm growth on neighbouring farms25 July 2022 | Journal of Agricultural Economics, Vol. 4 Cross Ref Multimodel Errors and Emergence Times in Climate Attribution StudiesJournal of Climate, Vol. 35, No. 14 Cross Ref The hierarchical structure of galactic haloes: generalized N -dimensional clustering with C lu STAR-ND20 June 2022 | Monthly Notices of the Royal Astronomical Society, Vol. 514, No. 4 Cross Ref Effective End-to-End Learning Framework for Economic DispatchIEEE Transactions on Network Science and Engineering, Vol. 9, No. 4 Cross Ref 4-D Gesture Sensing Using Reconfigurable Virtual Array Based on a 60-GHz FMCW MIMO Radar SensorIEEE Transactions on Microwave Theory and Techniques, Vol. 70, No. 7 Cross Ref Estimation of drift and diffusion functions from unevenly sampled time-series data27 July 2022 | Physical Review E, Vol. 106, No. 1 Cross Ref Detecting space–time patterns of disease risk under dynamic background population20 April 2022 | Journal of Geographical Systems, Vol. 24, No. 3 Cross Ref Wind power prediction based on PSO-KalmanEnergy Reports, Vol. 8 Cross Ref Visual cluster separation using high-dimensional sharpened dimensionality reduction21 April 2022 | Information Visualization, Vol. 21, No. 3 Cross Ref Interval Wind-Speed Forecasting Model Based on Quantile Regression Bidirectional Minimal Gated Memory Network and Kernel Density Estimation17 June 2022 | Arabian Journal for Science and Engineering, Vol. 4 Cross Ref Spatio-temporal process monitoring using exponentially weighted spatial LASSO2 June 2022 | Journal of Quality Technology, Vol. 58 Cross Ref Bridge deformation prediction based on SHM data using improved VMD and conditional KDEEngineering Structures, Vol. 261 Cross Ref Nonparametric extrapolation of extreme quantiles: a comparison study7 October 2021 | Stochastic Environmental Research and Risk Assessment, Vol. 36, No. 6 Cross Ref Schedule Performance as a Baseline for the Experimental Analysis of Coordinated Behavior: Same or Different Units of Analysis?24 February 2022 | The Psychological Record, Vol. 72, No. 2 Cross Ref Rainfall intensity and catchment size control storm runoff in a gullied blanket peatlandJournal of Hydrology, Vol. 609 Cross Ref Creating a Healthy Environment for Children: GIS Tools for Improving the Quality of the Social Welfare Management System10 June 2022 | International Journal of Environmental Research and Public Health, Vol. 19, No. 12 Cross Ref Conditional catheter‐related thrombosis free probability and risk‐adapted choices of catheter for lung cancer13 May 2022 | Thoracic Cancer, Vol. 13, No. 12 Cross Ref Search for an anomalous excess of charged-current quasielastic νe interactions with the MicroBooNE experiment using Deep-Learning-based reconstruction13 June 2022 | Physical Review D, Vol. 105, No. 11 Cross Ref Spatio-temporal wind speed prediction based on Clayton Copula function with deep learning fusionRenewable Energy, Vol. 192 Cross Ref Dynamic disease screening by joint modelling of survival and longitudinal data27 May 2022 | Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 23 Cross Ref Uncertainties in the Assessment of COVID-19 Risk: A Study of People’s Exposure to High-Risk Environments Using Individual-Level Activity Data20 September 2021 | Annals of the American Association of Geographers, Vol. 112, No. 4 Cross Ref Incremental software product line verification - A performance analysis with dead variable code17 March 2022 | Empirical Software Engineering, Vol. 27, No. 3 Cross Ref Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstationary modelsJournal of Econometrics, Vol. 117 Cross Ref An Unconventional Technique for Choosing the Kernel Function Blur Coefficients in Nonparametric Regression18 August 2022 | Measurement Techniques, Vol. 65, No. 2 Cross Ref Specificities of ERD lateralization during motion execution Cross Ref Kernel density estimation for circular data: a Fourier series-based plug-in approach for bandwidth selection21 April 2022 | Journal of Nonparametric Statistics, Vol. 34, No. 2 Cross Ref Concurrent Effects between Geomagnetic Storms and Magnetospheric Substorms6 April 2022 | Universe, Vol. 8, No. 4 Cross Ref Deep non-crossing probabilistic wind speed forecasting with multi-scale featuresEnergy Conversion and Management, Vol. 257 Cross Ref Efficient and robust propensity‐score‐based methods for population inference using epidemiologic cohorts6 September 2021 | International Statistical Review, Vol. 90, No. 1 Cross Ref Estimation of a Nonlinear Functional of the Probability Density of a Three-Dimensional Random Variable to Improve the Computational Efficiency of Nonparametric Decision Rules28 August 2022 | Optoelectronics, Instrumentation and Data Processing, Vol. 58, No. 2 Cross Ref The relation between belief in a just world and early processing of deserved and undeserved outcomes: An ERP study13 February 2022 | Social Neuroscience, Vol. 17, No. 2 Cross Ref Mutual information scaling for tensor network machine learning20 January 2022 | Machine Learning: Science and Technology, Vol. 3, No. 1 Cross Ref Automatically extracting surfaces of reinforced concrete bridges from terrestrial laser scanning point cloudsAutomation in Construction, Vol. 135 Cross Ref OnlineSTLProceedings of the VLDB Endowment, Vol. 15, No. 7 Cross Ref On the application of generative adversarial networks for nonlinear modal analysisMechanical Systems and Signal Processing, Vol. 166 Cross Ref Interval Prediction Method for Solar Radiation Based on Kernel Density Estimation and Machine LearningComplexity, Vol. 2022 Cross Ref A three-step local smoothing approach for estimating the mean and covariance functions of spatio-temporal Data20 March 2021 | Annals of the Institute of Statistical Mathematics, Vol. 74, No. 1 Cross Ref Phase I monitoring of serially correlated nonparametric profiles by mixed‐effects modeling28 July 2021 | Quality and Reliability Engineering International, Vol. 38, No. 1 Cross Ref Data-driven prosumer-centric energy scheduling using convolutional neural networksApplied Energy, Vol. 308 Cross Ref The (un)predictable magnetosphere: the role of the internal dynamics3 March 2022 | Journal of Plasma Physics, Vol. 88, No. 1 Cross Ref Quick Selecting Kernel Blur Coefficients to Estimate Probability Density for Independent Random Variables8 July 2022 | Optoelectronics, Instrumentation and Data Processing, Vol. 58, No. 1 Cross Ref Robust analogs to the coefficient of variation20 August 2020 | Journal of Applied Statistics, Vol. 49, No. 2 Cross Ref Nonparametric Mass Imputation for Data Integration17 November 2020 | Journal of Survey Statistics and Methodology, Vol. 10, No. 1 Cross Ref Regional wind power probabilistic forecasting based on an improved kernel density estimation, regular vine copulas, and ensemble learningEnergy, Vol. 238 Cross Ref Probabilistic Revenue Analysis of Microgrid Considering Source-Load and Forecast UncertaintiesIEEE Access, Vol. 10 Cross Ref Data-Enhancement Strategies in Weather-Related Health Studies14 January 2022 | International Journal of Environmental Research and Public Health, Vol. 19, No. 2 Cross Ref Model-based techniques for traffic congestion detection Cross Ref Object-based cluster validation with densitiesPattern Recognition, Vol. 121 Cross Ref Towards Robust Waveform-Based Acoustic ModelsIEEE/ACM Transactions on Audio, Speech, and Language Processing, Vol. 30 Cross Ref Nonparametric Survival Analysis20 July 2022 Cross Ref A Combined Approach for Monitoring Monthly Surface Water/Ice Dynamics of Lesser Slave Lake Via Earth Observation DataIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 15 Cross Ref Structural characterisation of nanoalloys for (photo)catalytic applications with the Sapphire library1 January 2022 | Faraday Discussions, Vol. 8 Cross Ref Joint modeling of multivariate nonparametric longitudinal data and survival data: A local smoothing approach25 September 2021 | Statistics in Medicine, Vol. 40, No. 29 Cross Ref Shock Reduction Technique on Thin Plate Structure by Wave Refraction Using an Elastic PatchShock and Vibration, Vol. 2021 Cross Ref Persistent meanders and eddies lead to quasi-steady Lagrangian transport patterns in a weak western boundary current12 January 2021 | Scientific Reports, Vol. 11, No. 1 Cross Ref Caenorhabditis elegans exhibits positive gravitaxis14 September 2021 | BMC Biology, Vol. 19, No. 1 Cross Ref Niche partitioning among social clusters of a resident estuarine apex predator15 November 2021 | Behavioral Ecology and Sociobiology, Vol. 75, No. 12 Cross Ref Study of the Method for Verification of the Hypothesis on Independence of Two-Dimensional Random Quantities Using a Nonparametric Classifier13 May 2022 | Optoelectronics, Instrumentation and Data Processing, Vol. 57, No. 6 Cross Ref Epanechnikov kernel for PDF estimation applied to equalization and blind source separationSignal Processing, Vol. 189 Cross Ref Age-coherent extensions of the Lee–Carter model29 April 2021 | Scandinavian Actuarial Journal, Vol. 2021, No. 10 Cross Ref compaso : A new halo finder for competitive assignment to spherical overdensities19 October 2021 | Monthly Notices of the Royal Astronomical Society, Vol. 509, No. 1 Cross Ref Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model26 October 2021 | Mathematics, Vol. 9, No. 21 Cross Ref A method of sequentially generating a set of components of a multidimensional random variable using a nonparametric pattern recognition algorithm1 November 2021 | Computer Optics, Vol. 45, No. 6 Cross Ref Year-round spatial distribution and migration phenology of a rapidly declining trans-Saharan migrant—evidence of winter movements and breeding site fidelity in European turtle doves13 October 2021 | Behavioral Ecology and Sociobiology, Vol. 75, No. 11 Cross Ref Efficiency of European universities: A comparison of peersResearch Policy, Vol. 50, No. 9 Cross Ref Heads Or Tails: A Framework To Model Supply Chain Heterogeneous Messages Cross Ref Research of Wind Power Generation Characteristics in Southern China Based on Improved Non-Parametric Kernel Density Estimation Cross Ref Fast multivariate empirical cumulative distribution function with connection to kernel density estimationComputational Statistics & Data Analysis, Vol. 162 Cross Ref Some confidence intervals and insights for the proportion below the relative poverty line13 October 2021 | SN Business & Economics, Vol. 1, No. 10 Cross Ref The HARPS search for southern extra-solar planets18 October 2021 | Astronomy & Astrophysics, Vol. 654 Cross Ref The sectorally heterogeneous and time-varying price elasticities of energy demand in ChinaEnergy Economics, Vol. 102 Cross Ref Outlier accommodation with semiparametric density processes: A study of Antarctic snow density modelling29 September 2021 | Statistical Modelling, Vol. 124 Cross Ref SAFE-STOP System: Tactical Intention Awareness Based Emergency Collision Avoidance for Malicious Cut-in of Surrounding Vehicle Cross Ref Violin graphs to supervise the energy performance of PV arrays Cross Ref Application of a novel structure-adaptative grey model with adjustable time power item for nuclear energy consumption forecastingApplied Energy, Vol. 298 Cross Ref The continuous wavelet derived by smoothing function and its application in cosmology5 August 2021 | Communications in Theoretical Physics, Vol. 73, No. 9 Cross Ref Inertial Sensor Algorithms to Characterize Turning in Neurological Patients With Turn HesitationsIEEE Transactions on Biomedical Engineering, Vol. 68, No. 9 Cross Ref Consistent inference for predictive regressions in persistent economic systemsJournal of Econometrics, Vol. 224, No. 1 Cross Ref Identifying convergence in nitrogen oxides emissions from motor vehicles in China: A spatial panel data approachJournal of Cleaner Production, Vol. 316 Cross Ref Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation22 September 2021 | Journal of The Royal Society Interface, Vol. 18, No. 182 Cross Ref Nonparametric pattern recognition algorithm for testing a hypothesis of the independence of random variables1 September 2021 | Computer Optics, Vol. 5, No. 45 Cross Ref Noise and error analysis and optimization in particle-based kinetic plasma simulationsJournal of Computational Physics, Vol. 440 Cross Ref Unsupervised Learning Methods for Molecular Simulation Data4 May 2021 | Chemical Reviews, Vol. 121, No. 16 Cross Ref A robust dynamic screening system by estimation of the longitudinal data distribution26 May 2020 | Journal of Quality Technology, Vol. 53, No. 4 Cross Ref Ellipsoidal one-class constraint acquisition for quadratically constrained programmingEuropean Journal of Operational Research, Vol. 293, No. 1 Cross Ref Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experimentsReliability Engineering & System Safety, Vol. 212 Cross Ref Effective disease surveillance by using covariate information30 July 2021 | Statistics in Medicine, Vol. 59 Cross Ref Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models6 January 2021 | Journal of Time Series Analysis, Vol. 42, No. 4 Cross Ref between and to the of level and in the of in Research, Vol. 68, No. 2 Cross Ref energy demand spatio-temporal data Vol. Cross Ref Learning for Statistical of June 2021 | Vol. 29 Cross Ref joint distribution analysis of the under semiparametric distribution for the in of Engineering and Science, Vol. No. 2 Cross Ref model of Econometrics, Vol. No. 2 Cross Ref of Based on and Network with the Quantile May 2021 | Applied Vol. 11, No. 11 Cross Ref An to multivariate probabilistic and Vol. 4 Cross Ref based on deep learning model with attention for hybrid system under Energy, Vol. 170 Cross Ref and March 2022 | Mathematics, Vol. No. 1 Cross Ref Uncertainty Analysis of Wind Power Based on Data Cross Ref kernel density estimation Systems with Applications, Vol. Cross Ref network modelling of the of a with the Physics Vol. Cross Ref March 2021 | Journal of Computational and Vol. No. 2 Cross Ref modeling of for July 2020 | Reviews, Vol. 40, No. 3 Cross Ref for Cross Ref on the size of February 2021 | of the of Vol. No. 9 Cross Ref Uncertainty analysis of wind power probability density forecasting based on and quantile Vol. Cross Ref of Methods in Data of March 2021 | International Journal of Vol. 10, No. 3 Cross Ref Dynamic spatial analysis of China: and spatial convergence Research, Vol. No. 3 Cross Ref the Hypothesis of the Independence of Two-Dimensional Random Using a Nonparametric for August 2021 | Optoelectronics, Instrumentation and Data Processing, Vol. 57, No. 2 Cross Ref A Study of Nonparametric Kernel with of Vol. No. 1 Cross Ref Fast Modelling, Vol. Cross Ref for of Coefficients for Kernel of Probability March 2021 | Measurement Techniques, Vol. No. 11 Cross Ref of laser fusion Vol. Cross Ref A of density based clustering September 2020 | Frontiers of Computer Science, Vol. 15, No. 1 Cross Ref of Information and Regression for of Acoustic Data during on Structural and Construction, Vol. No. 1 Cross Ref of Heterogeneous in January 2021 | Research Vol. No. 2 Cross Ref for Time Series of Cross Ref Data-driven Kernel-based Probabilistic for Time Series Reduction Cross Ref The for Robust Energy Estimation Cross Ref from August 2020 Cross Ref during Chain for Detecting Using from 2020 | Vol. No. 1 Cross Ref Method for of in Using and 2020 | Remote Sensing, Vol. 13, No. 1 Cross Ref of a Framework for Environmental of 2020 | Journal of Science and Engineering, Vol. 9, No. 1 Cross Ref a for kernel density estimation, and of Vol. No. Cross Ref Analysis of the of the mean of the kernel probability density estimation in the of and random variables1 January 2021 | No. 3 Cross Ref Energy Management of April 2021 Cross Ref for Detecting of July 2021 Cross Ref of a Analysis Method to the of COVID-19 Kernel Density Estimation Using July 2021 Cross Ref On generative as the for August 2021 | Engineering, Vol. 2 Cross Ref and in the January 2021 | Journal of Vol. 27, No. 1 Cross Ref The in January 2021 | Vol. No. 5 Cross Ref Kernel Based for MIMO Radar in Access, Vol. 9 Cross Ref The diffusion of diffusion and Computational Analysis, Vol. Cross Ref of of components of a multidimensional random variable based on a nonparametric pattern recognition algorithm1 January 2021 | No. 9 Cross Ref in energy efficiency of and its for performance Journal of and Engineering, Vol. Cross Ref of Nonlinear Systems with Cross Ref Probability density forecasting of wind power based on quantile neural Systems, Vol. Cross Ref Hypothesis testing based on a of of Econometrics, Vol. No. 2 Cross Ref Analysis of distribution human in the of Lake in Vol. Cross Ref in and May 2020 | Scientific Reports, Vol. 10, No. 1 Cross Ref Assessment of regressions for in the insights from and historical June 2020 | Vol. 17, No. 12 Cross Ref hybrid and for September 2020 | Journal on Communications and Vol. No. 1 Cross Ref of March 2021 | Physics of Vol. No. 12 Cross Ref price and July 2020 | European Review of Agricultural Economics, Vol. No. 5 Cross Ref A of | Applied Vol. 27, No. Cross Ref Risk Estimation to and in November 2020 | Frontiers in Earth Science, Vol. 8 Cross Ref Learning to a A Transactions on Systems Technology, Vol. No. 6 Cross Ref for cell lung Analysis based on and Radiation Vol. Cross Ref Fast for the of the Kernel Density April 2021 | Optoelectronics, Instrumentation and Data Processing, Vol. No. 6 Cross Ref Using Deep Learning: With Systems and November 2020 | Journal of in Earth Systems, Vol. No. 11 Cross Ref search in the A Research Vol. Cross Ref A new algorithm based on and algorithm to the optimization Computing, Vol. Cross Ref of data methods and clustering model in the of of of Vol. No. 3 Cross Ref Energy Efficient in of Cross Ref Statistical of and for July 2020 | Journal International, Vol. No. 1 Cross Ref Unsupervised of Deep Bayesian Cross Ref for Visual of Data Cross Ref nonlinear of covariance Annals of Statistics, Vol. No. 5 Cross Ref modeling and prediction approach for using deep Journal of and Mass Vol. Cross Ref in model for May 2020 | Structural and Vol. No. 4 Cross Ref A Kernel Outlier August | Review, Vol. No. 5 Cross Ref emissions in China: spatial patterns and Research, Vol. 11, No. 9 Cross Ref A Analysis of the Effects of on the Performance of Transactions on Applications, Vol. No. 5 Cross Ref during A for the of based on September 2020 | Journal of and Management, Vol. No. 3 Cross Ref Dynamic risk assessment with network and clustering Engineering & System Safety, Vol. Cross Ref with exchange and Some from Modelling, Vol. Cross Ref A probabilistic verification application of random

Next article Random Matrices in PhysicsEugene P. WignerEugene P. Wignerhttps://doi.org/10.1137/1009001PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] C. E. Porter, C. E. Porter, Fluctuations of quantal spectraStatistical Theories of Spectra: Fluctuations, Academic Press, New York, 1965 Google Scholar[2] Madan Lal Mehta, Random matrices, Academic Press Inc., Boston, MA, 1991xviii+562 MR1083764 0780.60014 Google Scholar[3] J. Wishart, Generalized product moment distribution in samples, Biometrika, 20 A (1928), 32–52, (Correction: Ibid., 20 A (1928), p. 425.) CrossrefGoogle Scholar[4] R. A. Fisher, The sampling distribution of some statistics obtained from non-linear equations, Ann. Eugenics, 9 (1939), 238–249, (now Ann. Human Genetics) MR0001499 0022.37202 CrossrefGoogle Scholar[5] A. T. James, Normal multivariate analysis and the orthogonal group, Ann. Math. Statistics, 25 (1954), 40–75 MR0060779 0055.13203 CrossrefISIGoogle Scholar[6] Samuel S. Wilks, Mathematical statistics, A Wiley Publication in Mathematical Statistics, John Wiley & Sons Inc., New York, 1962xvi+644, Chap. XI MR0144404 0173.45805 Google Scholar[7] Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946xvi+575 MR0016588 0063.01014 Google Scholar[8A] Freeman J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Mathematical Phys., 3 (1962), 140–156 10.1063/1.1703773 MR0143556 0105.41604 CrossrefISIGoogle Scholar[8B] Freeman J. Dyson, Statistical theory of the energy levels of complex systems. II, J. Mathematical Phys., 3 (1962), 157–165 10.1063/1.1703774 MR0143557 0105.41604 CrossrefISIGoogle Scholar[8C] Freeman J. Dyson, Statistical theory of the energy levels of complex systems. III, J. Mathematical Phys., 3 (1962), 166–175 10.1063/1.1703775 MR0143558 0105.41604 CrossrefISIGoogle Scholar[9] B. O. Koopman, Hamiltonian systems and transformations in Hilbert space, Proc. Nat. Acad. Sci. U.S.A., 17 (1931), 315–318 0002.05701 CrossrefGoogle Scholar[10] J. Von Neumann, Proof of the quasi-ergodic hypothesis, Proc. Nat. Acad. Sci. U.S.A., 18 (1932), 70–82 0004.31004 CrossrefGoogle Scholar[11] G. D. Birkhoff, Proof of a recurrence theorem for strongly transitive systems, Proc. Nat. Acad. Sci. U.S.A., 17 (1931), 650–655 0003.25601 CrossrefGoogle Scholar[12] G. D. Birkhoff, Proof of the ergodic theorem, Proc. Nat. Acad. Sci. U.S.A., 17 (1931), 656–660 0003.25602 CrossrefGoogle Scholar[13] G. D. Birkhoff and , B. O. Koopman, Recent contributions to the ergodic theory, Proc. Nat. Acad. Sci. U.S.A., 18 (1932), 279–282 0004.31102 CrossrefGoogle Scholar[14] Eugene P. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. of Math. (2), 62 (1955), 548–564 MR0077805 0067.08403 CrossrefISIGoogle Scholar[15] Eugene P. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. of Math. (2), 67 (1958), 325–327 MR0095527 0085.13203 CrossrefISIGoogle Scholar[16] Mark Kac, Probability and related topics in physical sciences, With special lectures by G. E. Uhlenbeck, A. R. Hibbs, and B. van der Pol. Lectures in Applied Mathematics. Proceedings of the Summer Seminar, Boulder, Colo., Vol. 1957, Interscience Publishers, London-New York, 1959, 11– MR0102849 0087.33003 Google Scholar[17] Burt V. Bronk, Accuracy of the semicircle approximation for the density of eigenvalues of random matrices, J. Mathematical Phys., 5 (1964), 215–220, (Also Princeton dissertation, 1963.) 10.1063/1.1704111 MR0161680 CrossrefISIGoogle Scholar[18] P. L. Hsu, On the distribution of roots of certain determinantal equations, Ann. Eugenics, 9 (1939), 250–258, (now Ann. Human Genetics) MR0001500 0022.24502 CrossrefGoogle Scholar[19] D. N. Nanda, Distribution of a root of a determinantal equation, Ann. Math. Statistics, 19 (1948), 47–57 MR0024106 0041.44903 CrossrefISIGoogle Scholar[20] Charles E. Porter and , Norbert Rosenzweig, Statistical properties of atomic and nuclear spectra, Ann. Acad. Sci. Fenn. Ser. A VI No., 44 (1960), 66–, (Also reprinted in [1] above.) MR0118377 0092.23304 Google Scholar[21] J. Von Neumann, Charakterisierung des Spectrums eines Integraloperators, Actualités Sci. Indust. (229), (1935), , (Reprinted in John von Neumann Collected Works, vol. IV, A. H. Taub, ed., Pergamon Press, New York, 1962.) Google Scholar[22] J. M. Blatt and , V. F. Weisskopf, Theoretical Nuclear Physics, John Wiley, New York, 1952, VIII-6 0049.14005 Google Scholar[23] T. D. Newton, Shell effects on the spacing of nuclear levels, Canad. J. Phys, 34 (1956), 804–829 0071.43106 CrossrefISIGoogle Scholar[24] Jean Ginibre, Statistical ensembles of complex, quaternion, and real matrices, J. Mathematical Phys., 6 (1965), 440–449 10.1063/1.1704292 MR0173726 0127.39304 CrossrefISIGoogle Scholar[25] Eugene P. Wigner, On a class of analytic functions from the quantum theory of collisions, Ann. of Math. (2), 53 (1951), 36–67 MR0039059 0042.45205 CrossrefISIGoogle Scholar[26] J. Von Neumann and , E. P. Wigner, Behavior of eigenvalues in adiabatic processes, Phys. Zeitschr., 30 (1929), 467–470 Google Scholar[27] M. L. Mehta, On the statistical properties of the level-spacings in nuclear spectra, Nuclear Phys., 18 (1960), 395–419 10.1016/0029-5582(60)90413-2 MR0112645 0107.44604 CrossrefISIGoogle Scholar[28] M. Gaudin, Sur la loi limite de l'espacement des valeurs propres d'une matrice aléatoire, Nuclear Phys., 25 (1961), 447–458 10.1016/0029-5582(61)90176-6 0107.44605 CrossrefISIGoogle Scholar[29] Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959, 104–105 MR0106295 0089.27501 Google Scholar[30] J. M. C. Scott, Neutron widths and the density of nuclear levels, Philos. Mag., 45 (1954), 1322–1331 0056.44707 CrossrefISIGoogle Scholar[31] C. E. Porter and , R. G. Thomas, Fluctuations of nuclear reaction widths, Phys. Rev., 104 (1956), 483–491 10.1103/PhysRev.104.483 CrossrefISIGoogle Scholar[32] N. Rosenzweig, Anomalous statistics of partial radiation widths, Phys. Lett., 6 (1963), 123–125 10.1016/0031-9163(63)90247-6 CrossrefISIGoogle Scholar Next article FiguresRelatedReferencesCited byDetails A mathematical perspective on edge-centric brain functional connectivity16 May 2022 | Nature Communications, Vol. 13, No. 1 Cross Ref Imaging and computing with disorder8 September 2022 | Nature Physics, Vol. 18, No. 9 Cross Ref Multivariate Statistical Analysis of Interaction Mechanism and Identity in Multiethnic Community Based on Random MatrixMathematical Problems in Engineering, Vol. 2022 Cross Ref Defining hierarchical protein interaction networks from spectral analysis of bacterial proteomes17 August 2022 | eLife, Vol. 11 Cross Ref Disordered Complex Networks: Energy Optimal Lattices and Persistent HomologyIEEE Transactions on Information Theory, Vol. 68, No. 8 Cross Ref On the Vectorial Property of Stochastic Dyadic Green's Function in Complex Electronic Enclosures Cross Ref Integrability of the ν=4/3 fractional quantum Hall edge states14 June 2022 | Quantum, Vol. 6 Cross Ref Coulomb and Riesz gases: The known and the unknownJournal of Mathematical Physics, Vol. 63, No. 6 Cross Ref Level Compressibility of Certain Random Unitary Matrices7 June 2022 | Entropy, Vol. 24, No. 6 Cross Ref Functional renormalization group for multilinear disordered Langevin dynamics I Formalism and first numerical investigations at equilibrium5 May 2022 | Journal of Physics Communications, Vol. 6, No. 5 Cross Ref Random matrix theory for quantum and classical metastability in local Liouvillians6 May 2022 | Physical Review B, Vol. 105, No. 18 Cross Ref Supercell symmetry modified spectral statistics of Kramers-Weyl fermions27 April 2022 | Journal of Physics A: Mathematical and Theoretical Cross Ref Quantum kicked rotor and its variants: Chaos, localization and beyondPhysics Reports, Vol. 956 Cross Ref Eigenvalues of Random Matrices with Generalized Correlations: A Path Integral Approach22 March 2022 | Physical Review Letters, Vol. 128, No. 12 Cross Ref Optimal delocalization for generalized Wigner matricesAdvances in Mathematics, Vol. 396 Cross Ref Spectral crossovers and universality in quantum spin chains coupled to random fields21 January 2022 | Physical Review B, Vol. 105, No. 1 Cross Ref On the Statistical Analysis of Space-Time Wave Physics in Complex Enclosures Cross Ref Probing Many-Body Systems near Spectral Degeneracies26 September 2021 | Symmetry, Vol. 13, No. 10 Cross Ref Random Matrix Theory and Its ApplicationsStatistical Science, Vol. 36, No. 3 Cross Ref Generic features in the spectral decomposition of correlation matricesJournal of Mathematical Physics, Vol. 62, No. 8 Cross Ref Self-Assembly of Biomolecular Condensates with Shared Components24 June 2021 | Physical Review Letters, Vol. 126, No. 25 Cross Ref Quantized dynamics in closed quantum systems23 April 2021 | Journal of Physics A: Mathematical and Theoretical, Vol. 54, No. 20 Cross Ref Dimension-free bounds for largest singular values of matrix Gaussian series26 September 2019 | Communications in Statistics - Theory and Methods, Vol. 50, No. 10 Cross Ref The identification of $${{\varvec{\alpha }}}$$-clustered doorway states in $$^{44,48,52}$$Ti using machine learning29 March 2021 | The European Physical Journal A, Vol. 57, No. 3 Cross Ref Accuracy and precision of the estimation of the number of missing levels in chaotic spectra using long-range correlations27 February 2021 | The European Physical Journal Plus, Vol. 136, No. 2 Cross Ref The snap, crackle and pop of solar flares explainedBrazilian Journal of Probability and Statistics, Vol. 35, No. 1 Cross Ref Low rattling: A predictive principle for self-organization in active collectives31 December 2020 | Science, Vol. 371, No. 6524 Cross Ref Manifestations of Chaos in Quantum Scattering Processes8 February 2021 Cross Ref Nuclear energy level complexity: Fano factor signature of chaotic behavior of nearest-neighbor time-series analysis1 October 2020 | Physical Review C, Vol. 102, No. 4 Cross Ref Spectral statistics of random Toeplitz matrices6 October 2020 | Physical Review E, Vol. 102, No. 4 Cross Ref Applications of the Random Coupling Model for stacked printed circuit boards Cross Ref A Perspective on Correlation-Based Financial Networks and Entropy Measures25 August 2020 | Frontiers in Physics, Vol. 8 Cross Ref Notes on matrix models (matrix musings)24 August 2020 | Journal of Statistical Mechanics: Theory and Experiment, Vol. 2020, No. 8 Cross Ref Effect of interpopulation spike-timing-dependent plasticity on synchronized rhythms in neuronal networks with inhibitory and excitatory populations17 March 2020 | Cognitive Neurodynamics, Vol. 14, No. 4 Cross Ref Gaussian determinantal processes: A new model for directionality in data1 June 2020 | Proceedings of the National Academy of Sciences, Vol. 117, No. 24 Cross Ref Key Factors Analysis of Line Loss Rates in Transformer Regions Based on Random Matrix Theory Cross Ref A Stochastic Green’s Function for Solution of Wave Propagation in Wave-Chaotic EnvironmentsIEEE Transactions on Antennas and Propagation, Vol. 68, No. 5 Cross Ref Perspectives on relativistic quantum chaos6 March 2020 | Communications in Theoretical Physics, Vol. 72, No. 4 Cross Ref Finite-range Coulomb gas models. I. Some analytical results24 February 2020 | Physical Review E, Vol. 101, No. 2 Cross Ref Finite-range Coulomb gas models. II. Applications to quantum kicked rotors and banded random matrices24 February 2020 | Physical Review E, Vol. 101, No. 2 Cross Ref Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant19 June 2020 Cross Ref The brain-derived neurotrophic factor Val66Met polymorphism increases segregation of structural correlation networks in healthy adult brains5 August 2020 | PeerJ, Vol. 8 Cross Ref Extracting the spectral signature of α clustering in Ti44,48,52 using a continuous wavelet transform15 November 2019 | Physical Review C, Vol. 100, No. 5 Cross Ref A Time Sequence Data Processing Method Based on Random Matrix of Smart Electric Meter Cross Ref May's instability in large economies18 September 2019 | Physical Review E, Vol. 100, No. 3 Cross Ref Asymmetry in repeated isotropic rotations10 September 2019 | Physical Review Research, Vol. 1, No. 2 Cross Ref Dynamical Thermalization of Interacting Fermionic Atoms in a Sinai Oscillator Trap8 August 2019 | Condensed Matter, Vol. 4, No. 3 Cross Ref Altered Domain Functional Network Connectivity Strength and Randomness in Schizophrenia23 July 2019 | Frontiers in Psychiatry, Vol. 10 Cross Ref A Novel Statistical Model for the Electromagnetic Coupling to Electronics inside Enclosures Cross Ref Novel techniques for constraining neutron-capture rates relevant for r-process heavy-element nucleosynthesisProgress in Particle and Nuclear Physics, Vol. 107 Cross Ref Disorder-induced topological transition in porous media flow networksJournal of Non-Newtonian Fluid Mechanics, Vol. 268 Cross Ref Toward the Unification of Physics and Number Theory28 November 2019 | Reports in Advances of Physical Sciences, Vol. 03, No. 01 Cross Ref Ecological persistence, incumbency and reorganization in the Karoo Basin during the Permian-Triassic transitionEarth-Science Reviews, Vol. 189 Cross Ref Complex Market Dynamics in the Light of Random Matrix Theory3 April 2019 Cross Ref Interacting quantum walk on a graph16 January 2019 | Physical Review E, Vol. 99, No. 1 Cross Ref Will a Large Economy Be Stable?SSRN Electronic Journal Cross Ref Spatiotemporal Big Data Analysis for Smart Grids Based on Random Matrix Theory21 December 2018 Cross Ref Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole18 October 2018 | The European Physical Journal B, Vol. 91, No. 10 Cross Ref A Stochastic Green’s Function - Integral Equation Method for Communication in Diffuse Multipath Environments Cross Ref Marginally stable equilibria in critical ecosystems31 August 2018 | New Journal of Physics, Vol. 20, No. 8 Cross Ref Effects of a strong magnetic field on internal gravity waves: trapping, phase mixing, reflection, and dynamical chaos12 April 2018 | Monthly Notices of the Royal Astronomical Society, Vol. 477, No. 4 Cross Ref Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domainsThe Journal of Chemical Physics, Vol. 148, No. 20 Cross Ref Abelian tensor models on the lattice16 April 2018 | Physical Review D, Vol. 97, No. 8 Cross Ref Quantum Stochastic Trajectories: The Fokker–Planck–Bohm Equation Driven by the Reduced Density Matrix21 February 2018 | The Journal of Physical Chemistry A, Vol. 122, No. 10 Cross Ref A novel stochastic integral equation method for wireless communication in diffuse multipath environments Cross Ref On the spectral unfolding of chaotic and mixed systemsPhysica A: Statistical Mechanics and its Applications, Vol. 492 Cross Ref Quantum stochastic trajectories: the Smoluchowski–Bohm equation1 January 2018 | Physical Chemistry Chemical Physics, Vol. 20, No. 1 Cross Ref Diluted banded random matrices: scaling behavior of eigenfunction and spectral properties16 November 2017 | Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 49 Cross Ref Alteration of soil bacterial interaction networks driven by different long-term fertilization management practices in the red soil of South ChinaApplied Soil Ecology, Vol. 120 Cross Ref Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors16 November 2017 | Physical Review E, Vol. 96, No. 5 Cross Ref A novel stochastic wave model statistically replicating reverberation chambers Cross Ref Statistical behavior of time dynamics evolution of HIV infectionPhysics Letters A, Vol. 381, No. 35 Cross Ref Kolmogorov Turbulence Defeated by Anderson Localization for a Bose-Einstein Condensate in a Sinai-Oscillator Trap2 August 2017 | Physical Review Letters, Vol. 119, No. 5 Cross Ref Quantitative statistical analysis with physics-based surrogate modeling for wave chaotic systems Cross Ref Asymptotic coincidence of the statistics for degenerate and non-degenerate correlated real Wishart ensembles12 May 2017 | Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 23 Cross Ref EM-CAD for complex electronics systems: A journey from order to chaos Cross Ref Fusion of first-principles and statistical analyses in complex electronics systems Cross Ref Light fields in complex media: Mesoscopic scattering meets wave control2 March 2017 | Reviews of Modern Physics, Vol. 89, No. 1 Cross Ref References11 February 2017 Cross Ref Fast Parallel Construction of Correlation Similarity Matrices for Gene Co-Expression Networks on Multicore ClustersProcedia Computer Science, Vol. 108 Cross Ref Dynamical thermalization in isolated quantum dots and black holes20 February 2017 | EPL (Europhysics Letters), Vol. 117, No. 1 Cross Ref Disordered quivers and cold horizons15 December 2016 | Journal of High Energy Physics, Vol. 2016, No. 12 Cross Ref Protein States as Symmetry Transitions in the Correlation Matrices1 November 2016 | The Journal of Physical Chemistry B, Vol. 120, No. 44 Cross Ref Targeting functional motifs of a protein family12 October 2016 | Physical Review E, Vol. 94, No. 4 Cross Ref Tracking and Data Fusion for Ground Surveillance2 September 2016 Cross Ref Reprint of : Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiardPhysica E: Low-dimensional Systems and Nanostructures, Vol. 82 Cross Ref A hybrid method for quantitative statistical analysis of in-situ IC and electronics in complex and wave-chaotic enclosures Cross Ref Dynamics and thermalization of a Bose-Einstein condensate in a Sinai-oscillator trap25 July 2016 | Physical Review A, Vol. 94, No. 1 Cross Ref Separating Putative Pathogens from Background Contamination with Principal Orthogonal Decomposition: Evidence for Leptospira in the Ugandan Neonatal Septisome13 June 2016 | Frontiers in Medicine, Vol. 3 Cross Ref Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices9 June 2016 | Physical Review E, Vol. 93, No. 6 Cross Ref RandNLACommunications of the ACM, Vol. 59, No. 6 Cross Ref Quantum Theory with a December | of Physics, Vol. No. 5 Cross Ref of number in May 2016 | Physical Review E, Vol. 93, No. 5 Cross Ref A quantitative statistical analysis of in-situ IC and electronics in complex and wave-chaotic enclosures Cross Ref Analysis of structural in a model liquid the eigenvalues and of the atomic Journal of Chemical Physics, Vol. No. 9 Cross Ref Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiardPhysica E: Low-dimensional Systems and Nanostructures, Vol. Cross Ref of Spectral Transitions for Interacting February 2016 | Physical Review Letters, Vol. No. 5 Cross Ref Random Matrix March 2016 Cross Ref on the March 2016 Cross Ref of the of the in by of Random Matrix Journal of Vol. No. 01 Cross Ref The of April 2016 Cross Ref Symmetry and dynamics universality of in quantum December | Physical Review B, Vol. No. 23 Cross Ref properties of the and and September | Physical Review C, Vol. No. 3 Cross Ref theory of Majorana and topological September | Reviews of Modern Physics, Vol. No. 3 Cross Ref The of February in a A: Statistical Mechanics and its Applications, Vol. Cross Ref Effect of Symmetry on Scattering from Majorana April | Physical Review Letters, Vol. No. Cross Ref spectral for random matrix ensembles with a June | Random Theory and Applications, Vol. No. Cross Ref of protein using January | and Vol. No. 3 Cross Ref of large wireless behavior using random matrix theory Cross Ref of October | Vol. No. 2 Cross Ref Quantum quantum chaos in the nuclear January | Journal of Series, Vol. Cross Ref Random Matrix Theory in dynamics Vol. Cross Ref January | Journal of Statistical Mechanics: Theory and Experiment, Vol. No. 1 Cross Ref Statistical and April 2016 | Vol. Cross Ref Spectral of in December | Physical Review A, Vol. No. 6 Cross Ref correlation of October | Journal of Number Theory, Vol. No. Cross Ref for on of the August | Physics, Vol. 24, No. 9 Cross Ref decoherence a to a random matrix August | Physical Review A, Vol. No. 2 Cross Ref the statistics of wave chaotic by the random A and Vol. No. 4 Cross Ref Dynamics in with by February | The Journal of Physical Chemistry A, Vol. No. 6 Cross Ref of the for chaotic and mixed systemsPhysica A: Statistical Mechanics and its Applications, Vol. 396 Cross Ref Tracking and Data Fusion for Ground January Cross Ref and Cross Ref of September Cross Ref to the of with Some Statistical Analysis of October Cross Ref A for Network Analysis Cross Ref in the spectra of nuclear energy December | Journal of Series, Vol. Cross Ref statistics of random December | Physical Review E, Vol. No. 6 Cross Ref of states for disordered systems from November | Physical Review B, Vol. No. 20 Cross Ref A method for spectral statistics on universality with an to the of the July | Journal of Physics A: Mathematical and Theoretical, Vol. No. 30 Cross Ref and Equation of the A, Vol. No. 3 Cross Ref Gene Co-Expression Network Construction and Random Matrix February | Vol. No. 2 Cross Ref analysis for functional and to Vol. Cross Ref May | Vol. 13, No. 1 Cross Ref Probability of Fluctuations in an Electromagnetic Transactions on Electromagnetic Vol. 54, No. 5 Cross Ref and effects in the nearest-neighbor for an June | Physical Review C, Vol. No. 6 Cross Ref Multivariate Statistical Analysis and Random Matrix September Cross Ref from spectra to Vol. No. 10 Cross Ref disordered media: matrix December | New Journal of Physics, Vol. 13, No. 12 Cross Ref Random matrix models for phase September | Reports on in Physics, Vol. No. 10 Cross Ref of HIV evolution of June | Proceedings of the National Academy of Sciences, Vol. No. Cross Ref eigenvalue of some complex correlated Wishart and random matricesJournal of Multivariate Vol. 102, No. 4 Cross Ref quantum Recent and to Reports, Vol. No. Cross Ref Level density and of March | Physical Review E, Vol. No. 3 Cross Ref Correlation of with January | Vol. No. Cross Ref of Random Matrix Theory to November Cross Ref Analysis of behavior on random matrix Vol. No. 4 Cross Ref Normal and von quantum ergodic May | Proceedings of the Royal Society A: Physical and Sciences, Vol. No. Cross Ref behavior of quantum September | The European Physical Journal Vol. 35, No. 2 Cross Ref and spectral in November | Letters, Vol. No. 6 Cross Ref of a energy July | New Journal of Physics, Vol. No. Cross Ref January | Journal of Modern Physics B, Vol. 24, No. Cross Ref Eigenvalue for a class of matrices with to May | Physical Review E, Vol. No. 5 Cross Ref The in Measuring the March | Physics, Vol. 3 Cross Ref correlation of of with Vol. No. Cross Ref A random matrix to December | Journal of Statistical Mechanics: Theory and Experiment, Vol. No. 12 Cross Ref Energy Localization in and The July | Chemical Reviews, Vol. No. 9 Cross Ref and structural of random brain networks with excitatory and inhibitory December | Journal of Vol. No. 1 Cross Ref correlation of on of Mathematical Analysis and Applications, Vol. No. 2 Cross Ref Random matrices for the August | Physical Review E, Vol. No. 2 Cross Ref On and of random hierarchical July | Journal of Statistical Mechanics: Theory and Experiment, Vol. No. Cross Ref Asymptotic Analysis of Cross Ref of random brain networks with excitatory and inhibitory Vol. 72, No. Cross Ref using random and Vol. 57, No. 3 Cross Ref spectral in and ensembles of random February | Physical Review E, Vol. No. 2 Cross Ref Eigenvalues of a of Random Matrices With to the Analysis of Transactions on Vol. 57, No. 2 Cross Ref and in the quantum dynamics of systems with February | Journal of and Theoretical Physics, Vol. No. 1 Cross Ref Spectral analysis of stochastic recurrence systems of equation and Stochastic Vol. No. 3 Cross Ref January | Journal of Modern Physics E, Vol. No. Cross Ref and July Cross Ref to and using random Transactions on and Electronic Vol. No. 3 Cross Ref eigenvalues of random May | Physical Review C, Vol. No. 5 Cross Ref the of in and Transactions on Engineering, Vol. No. 3 Cross Ref Statistical

Previous article Next article Approximate Integration of Stochastic Differential EquationsG. N. Mil'shtejnG. N. Mil'shtejnhttps://doi.org/10.1137/1119062PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. I. Gikhman and , A. V. Skorokhod, Introduction to the Theory of Random Processes, Izd-vo "Nauka", Moscow, 1965, (In Russian.) Google Scholar[2] I. I. Gikhman and , A. V. Skorokhod, Stochastic Differential Equations, Springer, New York, 1972 0242.60003 CrossrefGoogle Scholar[3] R. Z. Khas'minskii, Stability of Systems of Differential Equations under Random Perturbations of their Parameters, Izd-vo "Nauka", Moscow, 1969, (In Russian.) Google Scholar[4] E. Hills and , R. Phillips, Functional Analysis and Semigroups, American Mathematical Society, Providence, RI., 1957 0078.10004 Google Scholar[5] R. L. Stratonovich, Conditional Markov processes and their application to the theory of optimal control, Translated from the Russian by R. N. and N. B. McDonough for Scripta Technica, Inc. Modern Analytic and Computational Methods in Science and Mathematics, No. 7, American Elsevier Publishing Co., Inc., New York, 1968xvii+350 MR0221860 (36:4912) 0159.46804 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein schemeAIMS Mathematics, Vol. 8, No. 2 Cross Ref Impact of flow field resolution on produced water transport in Lagrangian and Eulerian modelsMarine Pollution Bulletin, Vol. 182 Cross Ref Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models19 April 2022 | Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 84, No. 4 Cross Ref Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry12 August 2022 | Entropy, Vol. 24, No. 8 Cross Ref Planktos: An Agent-Based Modeling Framework for Small Organism Movement and Dispersal in a Fluid Environment with Immersed Structures10 June 2022 | Bulletin of Mathematical Biology, Vol. 84, No. 7 Cross Ref Pricing path-dependent exotic options with flow-based generative networksApplied Soft Computing, Vol. 124 Cross Ref Estimation of drift and diffusion functions from unevenly sampled time-series data27 July 2022 | Physical Review E, Vol. 106, No. 1 Cross Ref The Generalized Gamma Distribution as a Useful RND under Heston's Stochastic Volatility Model26 May 2022 | Journal of Risk and Financial Management, Vol. 15, No. 6 Cross Ref On the approximation and simulation of iterated stochastic integrals and the corresponding Lévy areas in terms of a multidimensional Brownian motion26 May 2021 | Stochastic Analysis and Applications, Vol. 40, No. 3 Cross Ref Brownian particles driven by spatially periodic noise1 March 2022 | The European Physical Journal E, Vol. 45, No. 3 Cross Ref The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations23 February 2022 | Risks, Vol. 10, No. 3 Cross Ref 1 January 2022 Cross Ref Learning Stochastic Optimal Policies via Gradient DescentIEEE Control Systems Letters, Vol. 6 Cross Ref A Closed Form Solution for Pricing Variance Swaps Under the Rescaled Double Heston Model27 November 2021 | Computational Economics, Vol. 11 Cross Ref Cell-cell communication through FGF4 generates and maintains robust proportions of differentiated cell types in embryonic stem cells5 November 2021 | Development, Vol. 148, No. 21 Cross Ref On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model17 November 2021 | Mathematics, Vol. 9, No. 22 Cross Ref Mathematical modelling of the second wave of COVID-19 infections using deterministic and stochastic SIDR models7 July 2021 | Nonlinear Dynamics, Vol. 106, No. 2 Cross Ref A Local and Time Resolution of the COVID-19 Propagation—A Two-Dimensional Approach for Germany Including Diffusion Phenomena to Describe the Spatial Spread of the COVID-19 Pandemic7 July 2021 | Physics, Vol. 3, No. 3 Cross Ref Deep learning-based least squares forward-backward stochastic differential equation solver for high-dimensional derivative pricing26 March 2021 | Quantitative Finance, Vol. 21, No. 8 Cross Ref Information Transmission in Delay-Coupled Neuronal Circuits in the Presence of a Relay Population29 July 2021 | Frontiers in Systems Neuroscience, Vol. 15 Cross Ref Efficient simulation methods for the Quasi-Gaussian term-structure model with volatility smiles: practical applications of the KLNV-scheme4 February 2021 | Quantitative Finance, Vol. 21, No. 7 Cross Ref Convergence, non-negativity and stability of a new Lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model18 September 2020 | Japan Journal of Industrial and Applied Mathematics, Vol. 38, No. 2 Cross Ref Active noise-driven particles under space-dependent friction in one dimension4 May 2021 | Physical Review E, Vol. 103, No. 5 Cross Ref Transmission delays and frequency detuning can regulate information flow between brain regions15 April 2021 | PLOS Computational Biology, Vol. 17, No. 4 Cross Ref On the MS-stability of predictor–corrector schemes for stochastic differential equationsMathematics and Computers in Simulation, Vol. 180 Cross Ref Deep Splitting Method for Parabolic PDEsChristian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, and Ariel Neufeld13 September 2021 | SIAM Journal on Scientific Computing, Vol. 43, No. 5AbstractPDF (580 KB)A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line FailureJacob Roth, David A. Barajas-Solano, Panos Stinis, Jonathan Weare, and Mihai Anitescu25 January 2021 | Multiscale Modeling & Simulation, Vol. 19, No. 1AbstractPDF (39676 KB)Computing the finite time Lyapunov exponent for flows with uncertaintiesJournal of Computational Physics, Vol. 425 Cross Ref On the RND under Heston's Stochastic Volatility ModelSSRN Electronic Journal, Vol. 79 Cross Ref How Does Noise Help Robustness? Explanation and Exploration under the Neural SDE Framework Cross Ref Building a path-integral calculus: a covariant discretization approach18 November 2019 | Journal of Physics A: Mathematical and Theoretical, Vol. 52, No. 50 Cross Ref Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing17 July 2019 | Applied Mathematical Finance, Vol. 26, No. 3 Cross Ref A new delta expansion for multivariate diffusions via the Itô-Taylor expansionJournal of Econometrics, Vol. 209, No. 2 Cross Ref Variance swaps with double exponential Ornstein-Uhlenbeck stochastic volatilityThe North American Journal of Economics and Finance, Vol. 48 Cross Ref Stochastic simulation of anharmonic dissipation. II. Harmonic bath potentials with quadratic couplingsThe Journal of Chemical Physics, Vol. 150, No. 7 Cross Ref Gliotransmitter Exocytosis and Its Consequences on Synaptic Transmission22 January 2019 Cross Ref Modeling Neuron–Glia Interactions with the Brian 2 Simulator22 January 2019 Cross Ref Wave pinning in competition-diffusion models in variable environmentsJournal of Theoretical Biology, Vol. 461 Cross Ref Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative PricingSSRN Electronic Journal Cross Ref Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEsApplied Mathematics and Computation, Vol. 339 Cross Ref Preventing plunder: Military technology, capital accumulation, and economic growthJournal of Macroeconomics, Vol. 58 Cross Ref Numerical methods for simulation of stochastic differential equations15 January 2018 | Advances in Difference Equations, Vol. 2018, No. 1 Cross Ref Stationary moments, diffusion limits, and extinction times for logistic growth with random catastrophesJournal of Theoretical Biology, Vol. 454 Cross Ref Gaussian process approximations for fast inference from infectious disease dataMathematical Biosciences, Vol. 301 Cross Ref Phase drift on networks of coupled crystal oscillators for precision timing5 July 2018 | Physical Review E, Vol. 98, No. 1 Cross Ref Continuous-time smooth ambiguity preferencesJournal of Economic Dynamics and Control, Vol. 90 Cross Ref Generalized Green's function molecular dynamics for canonical ensemble simulations29 May 2018 | Physical Review E, Vol. 97, No. 5 Cross Ref Recursive marginal quantization of higher-order schemes19 January 2018 | Quantitative Finance, Vol. 18, No. 4 Cross Ref Diffusion Monte Carlo simulations of gas phase and adsorbed D 2 -(H 2 ) n clustersThe Journal of Chemical Physics, Vol. 148, No. 10 Cross Ref Application of Legendre spectral-collocation method to delay differential and stochastic delay differential equationAIP Advances, Vol. 8, No. 3 Cross Ref Finite variance unbiased estimation of stochastic differential equations Cross Ref A stochastic SIS epidemic model with vaccinationPhysica A: Statistical Mechanics and its Applications, Vol. 486 Cross Ref Forward, backward, and weighted stochastic bridges12 October 2017 | Physical Review E, Vol. 96, No. 4 Cross Ref Heat-Assisted Multiferroic Solid-State Memory25 August 2017 | Materials, Vol. 10, No. 9 Cross Ref Effects of correlations and fees in random multiplicative environments: Implications for portfolio management7 August 2017 | Physical Review E, Vol. 96, No. 2 Cross Ref Stochastic C-Stability and B-Consistency of Explicit and Implicit Milstein-Type Schemes19 September 2016 | Journal of Scientific Computing, Vol. 70, No. 3 Cross Ref Algorithms for integration of stochastic differential equations using parallel optimized sampling in the Stratonovich calculusComputer Physics Communications, Vol. 212 Cross Ref Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential EquationsM. Navarro Jimenez, O. P. Le Maître, and O. M. Knio18 April 2017 | SIAM/ASA Journal on Uncertainty Quantification, Vol. 5, No. 1AbstractPDF (1572 KB)Milstein-Type Procedures for Numerical Solutions of Stochastic Differential Equations with Markovian SwitchingSon L. Nguyen, Tuan A. Hoang, Dung T. Nguyen, and George Yin18 April 2017 | SIAM Journal on Numerical Analysis, Vol. 55, No. 2AbstractPDF (467 KB)Modeling Tools for Financial Options19 August 2017 Cross Ref Generating Random Numbers with Specified Distributions19 August 2017 Cross Ref Monte Carlo Simulation with Stochastic Differential Equations19 August 2017 Cross Ref Standard Methods for Standard Options19 August 2017 Cross Ref Finite-Element Methods19 August 2017 Cross Ref Pricing of Exotic Options19 August 2017 Cross Ref Beyond Black and Scholes19 August 2017 Cross Ref Preventing Plunder: Military Technology, Capital Accumulation, and Economic GrowthSSRN Electronic Journal Cross Ref Density Approximations for Multivariate Diffusions via an Itô-Taylor Expansion ApproachSSRN Electronic Journal Cross Ref A high-order discontinuous Galerkin method for Itô stochastic ordinary differential equationsJournal of Computational and Applied Mathematics, Vol. 308 Cross Ref Double-implicit and split two-step Milstein schemes for stochastic differential equations2 September 2015 | International Journal of Computer Mathematics, Vol. 93, No. 12 Cross Ref Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle26 October 2016 | Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 46 Cross Ref Synchronization detection in networks of coupled oscillators for pattern recognition Cross Ref Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds6 November 2015 | Annalen der Physik, Vol. 528, No. 5 Cross Ref Stochastic simplified modelling of abrasive waterjet footprints1 February 2016 | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, No. 2186 Cross Ref Parallel Optimized Sampling for Stochastic EquationsBogdan Opanchuk, Simon Kiesewetter, and Peter D. Drummond20 December 2016 | SIAM Journal on Scientific Computing, Vol. 38, No. 6AbstractPDF (1075 KB)Chebyshev spectral collocation method for stochastic delay differential equations8 April 2015 | Advances in Difference Equations, Vol. 2015, No. 1 Cross Ref An improved Milstein method for stiff stochastic differential equations1 December 2015 | Advances in Difference Equations, Vol. 2015, No. 1 Cross Ref Adaptive outer synchronization of delay-coupled nonidentical complex networks in the presence of intrinsic time delay and circumstance noise19 December 2014 | Nonlinear Dynamics, Vol. 80, No. 1-2 Cross Ref On the convergence of diffusion Monte Carlo in non-Euclidean spaces. I. Free diffusionThe Journal of Chemical Physics, Vol. 142, No. 11 Cross Ref On the convergence of diffusion Monte Carlo in non-Euclidean spaces. II. Diffusion with sources and sinksThe Journal of Chemical Physics, Vol. 142, No. 11 Cross Ref PC analysis of stochastic differential equations driven by Wiener noiseReliability Engineering & System Safety, Vol. 135 Cross Ref Modelling of Langevin Equations by the Method of Multiple ScalesIFAC-PapersOnLine, Vol. 48, No. 1 Cross Ref Computational solution of stochastic differential equations20 August 2013 | WIREs Computational Statistics, Vol. 5, No. 5 Cross Ref Stochastic modeling of the full cycle of one-product macroeconomy of growth27 March 2013 | Cybernetics and Systems Analysis, Vol. 49, No. 2 Cross Ref The Langevin and Fokker–Planck Equations in Polymer Rheology Cross Ref Time-Step Considerations in Particle Simulation Algorithms for Coulomb Collisions in PlasmasIEEE Transactions on Plasma Science, Vol. 38, No. 9 Cross Ref Ergodicity of the Stochastic Nosé–Hoover Heat BathJournal of the Physical Society of Japan, Vol. 79, No. 7 Cross Ref The foundations of a unified approach to mathematical modelling of angiogenesis31 October 2009 | International Journal of Advances in Engineering Sciences and Applied Mathematics, Vol. 1, No. 1 Cross Ref Weak forms of the locally transversal linearization (LTL) technique for stochastically driven nonlinear oscillatorsApplied Mathematical Modelling, Vol. 32, No. 9 Cross Ref Evolution of Compact Binary Populations in Globular Clusters: A Boltzmann Study. II. Introducing StochasticityThe Astrophysical Journal, Vol. 680, No. 2 Cross Ref Approximation Schemes for Stochastic Differential Equations in Hilbert SpaceYu. S. Mishura and G. M. Shevchenko28 August 2007 | Theory of Probability & Its Applications, Vol. 51, No. 3AbstractPDF (195 KB)Accurate Integration of Stochastic Climate Models with Application to El NiñoMonthly Weather Review, Vol. 132, No. 1 Cross Ref Quiet direct simulation of coulomb collisionsIEEE Transactions on Plasma Science, Vol. 31, No. 1 Cross Ref Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motionsThe Annals of Applied Probability, Vol. 11, No. 2 Cross Ref A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate VolatilitySSRN Electronic Journal Cross Ref A Nonparametric Analysis of the Forward Rate VolatilitiesSSRN Electronic Journal Cross Ref Statistical-mechanically exact simulation of polymer conformation in an external fieldThe Journal of Chemical Physics, Vol. 107, No. 15 Cross Ref Stability Analysis of Numerical Schemes for Stochastic Differential EquationsYoshihiro Saito and Taketomo Mitsui1 August 2006 | SIAM Journal on Numerical Analysis, Vol. 33, No. 6AbstractPDF (1444 KB)Approximation of Lyapunov Exponents of Nonlinear Stochastic Differential EquationsAxel Grorud and Denis Talay5 July 2006 | SIAM Journal on Applied Mathematics, Vol. 56, No. 2AbstractPDF (2423 KB)Approximation of the Zakai Equation for Nonlinear FilteringKazufumi Ito1 August 2006 | SIAM Journal on Control and Optimization, Vol. 34, No. 2AbstractPDF (1181 KB)Effects of distributed delays on the stability of structures under seismic excitation and multiplicative noiseSadhana, Vol. 20, No. 2-4 Cross Ref Numerical procedures for sample structures on stochastic differential equationsJournal of Mathematical Physics, Vol. 31, No. 8 Cross Ref Models of Chemical Gradient Sensing by Cells Cross Ref A Theorem on the Order of Convergence of Mean-Square Approximations of Solutions of Systems of Stochastic Differential EquationsG. N. Mil–shtein17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 4AbstractPDF (412 KB)Weak Approximation of Solutions of Systems of Stochastic Differential EquationsG. N. Mil'shtein28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 4AbstractPDF (1203 KB)Piecewise Constant Approximation for the Monte-Carlo Calculation of Wiener IntegralsA. D. Vent-Tsel', S. A. Gladyshev, and G. N. Mil'shteyn17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 4AbstractPDF (700 KB)Numerical Treatment of Stochastic Differential EquationsW. Rüemelin31 July 2006 | SIAM Journal on Numerical Analysis, Vol. 19, No. 3AbstractPDF (835 KB)A Method of Second-Order Accuracy Integration of Stochastic Differential EquationsG. N. Mil'shtein17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 2AbstractPDF (451 KB)Brownian dynamics study of transitions in a polymer chain of bistable oscillatorsThe Journal of Chemical Physics, Vol. 69, No. 3 Cross Ref Computational field theory and pattern formation Cross Ref Volume 19, Issue 3| 1975Theory of Probability & Its Applications History Submitted:23 September 1973Published online:28 July 2006 InformationCopyright © 1975 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119062Article page range:pp. 557-562ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Previous article Next article A Least Squares Estimate of Satellite AttitudeGrace WahbaGrace Wahbahttps://doi.org/10.1137/1007077PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"A Least Squares Estimate of Satellite Attitude." SIAM Review, 7(3), p. 409 Previous article Next article FiguresRelatedReferencesCited byDetails Multi-view clustering with orthogonal mapping and binary graphExpert Systems with Applications, Vol. 213 Cross Ref Rotational State Determination16 April 2022 Cross Ref Discrete-Time Rigid Body Pose Estimation Based on Lagrange–d’Alembert Principle14 September 2022 | Journal of Nonlinear Science, Vol. 32, No. 6 Cross Ref Attitude estimation of connected drones based on extended Kalman filter under real outdoor environments27 October 2022 | Advanced Robotics, Vol. 73 Cross Ref Numerical strategies for recursive least squares solutions to the matrix equation AX = B21 October 2022 | International Journal of Computer Mathematics, Vol. 162 Cross Ref Probing disorder in 2CzPN using core and valence states1 January 2022 | Physical Chemistry Chemical Physics, Vol. 24, No. 38 Cross Ref Direct measurement of vorticity using tracer particles with internal markers13 October 2022 | Experiments in Fluids, Vol. 63, No. 10 Cross Ref Best-fit constraint equations for coupling mixed-dimension simulation models with wide flange cross sectionsFinite Elements in Analysis and Design, Vol. 208 Cross Ref Optimization-Based Strapdown Attitude Alignment for High-Accuracy Systems: Covariance Analysis With ApplicationsIEEE Transactions on Aerospace and Electronic Systems, Vol. 58, No. 5 Cross Ref Partially latent factors based multi‐view subspace learning23 June 2022 | Computational Intelligence, Vol. 38, No. 5 Cross Ref Attitude Estimation and Control30 September 2022 Cross Ref References26 August 2022 Cross Ref A linear surrogate for optimising functions of an orthogonal matrix with applications in wave function theory26 September 2022 | Molecular Physics Cross Ref Research on Algorithms for Multi-Vector Attitude DeterminationMathematical Problems in Engineering, Vol. 2022 Cross Ref A high-accuracy initial alignment method based on backtracking process for strapdown inertial navigation systemMeasurement, Vol. 201 Cross Ref Absolute Triangulation Algorithms for Space Exploration1 September 2022 | Journal of Guidance, Control, and Dynamics, Vol. 3 Cross Ref Observability of the relative motion from inertial data in kinematic chainsControl Engineering Practice, Vol. 125 Cross Ref Robust Hybrid Attitude and Gyro-Bias Observer on QuaternionsIEEE Transactions on Industrial Electronics, Vol. 69, No. 8 Cross Ref A Gyroless Attitude Estimation for Ground Vehicle Under Severe Dynamic ConditionsIEEE Transactions on Intelligent Transportation Systems, Vol. 23, No. 8 Cross Ref Research on Gradient-Descent Extended Kalman Attitude Estimation Method for Low-Cost MARG9 August 2022 | Micromachines, Vol. 13, No. 8 Cross Ref Review of Calibration Methods for Asteroid Optical Cameras Cross Ref Low-cost Raspberry Pi star sensor for small satellitesJournal of Astronomical Telescopes, Instruments, and Systems, Vol. 8, No. 03 Cross Ref The role of ball backspin alignment and variability in basketball shooting accuracy25 May 2022 | Journal of Sports Sciences, Vol. 40, No. 12 Cross Ref QUEST Aided EKF for Attitude and Rate Estimation Using Modified Rodrigues Parameters16 June 2022 | WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL, Vol. 17 Cross Ref Design and analysis of attitude observers based on the Lagrange-d’Alembert principle applied to constrained three-vehicle formationsAdvances in Space Research, Vol. 69, No. 11 Cross Ref ARCS: Accurate Rotation and Correspondence Search Cross Ref On-Orbit Geometric Distortion Correction on Star Images through 2D Legendre Neural Network11 June 2022 | Remote Sensing, Vol. 14, No. 12 Cross Ref Implementation Features of Attitude Determination Algorithm for the SamSat-ION Nanosatellite Cross Ref Comparison of TRIAD+EKF and TRIAD+UKF Algorithms for Nanosatellite Attitude Estimation4 May 2022 | WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL, Vol. 17 Cross Ref Attitude estimation for artillery shells using magnetometers and frequency detection of accelerometersControl Engineering Practice, Vol. 122 Cross Ref Alignment and integration of spatial transcriptomics data16 May 2022 | Nature Methods, Vol. 19, No. 5 Cross Ref Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation20 May 2022 | Sensors, Vol. 22, No. 10 Cross Ref Canonical Face EmbeddingsIEEE Transactions on Biometrics, Behavior, and Identity Science, Vol. 4, No. 2 Cross Ref Robust optimal attitude determination using interval analysisAdvances in Space Research, Vol. 69, No. 6 Cross Ref Applications of a Single-Vector Inertial Aiding Scheme for 3U CubeSatsJournal of Spacecraft and Rockets, Vol. 59, No. 2 Cross Ref A Spacecraft Attitude Determination and Control Algorithm for Solar Arrays Pointing Leveraging Sun Angle and Angular Rates Measurements18 January 2022 | Algorithms, Vol. 15, No. 2 Cross Ref Fault Tolerant Attitude and Orbit Determination System for Small Satellite Platforms19 January 2022 | Aerospace, Vol. 9, No. 2 Cross Ref A Factor Graph-Based Attitude Determination Approach for Microsatellite with Star Sensor and Gyros18 January 2022 Cross Ref Regression Models for Directional Variables16 June 2022 Cross Ref Modelling the Movement of Magnetic North16 June 2022 Cross Ref Feasibility Study of Neural Network in Satellite Attitude Determination6 July 2022 Cross Ref Combined Attitude Determination for Real-Time Geomagnetic NavigationIEEE Magnetics Letters, Vol. 13 Cross Ref RANSIC: Fast and Highly Robust Estimation for Rotation Search and Point Cloud Registration Using Invariant CompatibilityIEEE Robotics and Automation Letters, Vol. 7, No. 1 Cross Ref An Improved In-flight Alignment Method Based on Backtracking Navigation for GPS-aided Low Cost SINS With Short EnduranceIEEE Robotics and Automation Letters, Vol. 7, No. 1 Cross Ref Joint Estimation of Stellar Atmospheric Refraction and Star Tracker AttitudeIEEE Transactions on Instrumentation and Measurement, Vol. 71 Cross Ref A New Instantaneous Method for Attitude Determination Using GPS Phase MeasurementIEEE Transactions on Instrumentation and Measurement, Vol. 71 Cross Ref Constrained Wrapped Least Squares: A Tool for High-Accuracy GNSS Attitude DeterminationIEEE Transactions on Instrumentation and Measurement, Vol. 71 Cross Ref Adaptive Attitude Estimation Using a Hybrid Model-Learning ApproachIEEE Transactions on Instrumentation and Measurement, Vol. 71 Cross Ref IEEE Transactions on Network Science and Engineering, Vol. 9, No. 4 Cross Ref Asymptotically stable optimal multi-rate rigid body attitude estimation based on lagrange-d'alembert principleJournal of Geometric Mechanics, Vol. 15, No. 1 Cross Ref Statistical confidence domain data driven based fast in-flight alignment methodMeasurement, Vol. 188 Cross Ref Nonlinear Attitude Estimation Using Intermittent Linear Velocity and Vector Measurements Cross Ref Variational Symplectic Accelerated Optimization on Lie Groups Cross Ref Global exponential angular velocity estimation of rigid-body spacecraft from quaternion and vector measurementsAerospace Science and Technology, Vol. 119 Cross Ref Multiplicative-modified-Rodrigues-parameters-based strong tracking unscented Kalman filter for satellite attitude estimation3 November 2021 | Measurement Science and Technology Cross Ref Planet–Sun Sensor RevisitedJournal of Spacecraft and Rockets, Vol. 58, No. 6 Cross Ref Assessments of bilateral asymmetry with application in human skull analysis6 October 2021 | PLOS ONE, Vol. 16, No. 10 Cross Ref Finite-time stable estimator for attitude motion in the presence of bias in angular velocity measurementsAutomatica, Vol. 132 Cross Ref Lessons Learned: Consider the ContextJournal of Applied Biomechanics, Vol. 37, No. 5 Cross Ref A Fast and Robust Rotation Search and Point Cloud Registration Method for 2D Stitching and 3D Object Localization19 October 2021 | Applied Sciences, Vol. 11, No. 20 Cross Ref Static Attitude Determination Using Convolutional Neural Networks26 September 2021 | Sensors, Vol. 21, No. 19 Cross Ref Attitude Estimation of SINS on Dynamic Base With Decoupling Gravity VectorIEEE Sensors Journal, Vol. 21, No. 18 Cross Ref Evaluation of Gradient Descent Algorithm for Attitude Estimation Cross Ref A super-fast optimal attitude matrix in attitude determination7 June 2021 | Measurement Science and Technology, Vol. 32, No. 9 Cross Ref Passive and Explicit Attitude and Gyro-Bias Observers Using Inertial MeasurementsIEEE Transactions on Industrial Electronics, Vol. 68, No. 9 Cross Ref Interlaced Attitude Estimation for Spacecraft Using Vector Observations19 October 2021 | Guidance, Navigation and Control, Vol. 01, No. 03 Cross Ref Robust and efficient forward, differential, and inverse kinematics using dual quaternions20 July 2020 | The International Journal of Robotics Research, Vol. 40, No. 10-11 Cross Ref High Update Rate Attitude Measurement Method of Star Sensors Based on Star Point Correction of Rolling Shutter Exposure25 August 2021 | Sensors, Vol. 21, No. 17 Cross Ref Bibliography7 May 2021 Cross Ref Fault-tolerant control of flexible satellite with magnetic actuation and reaction wheel24 August 2021 | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 105592 Cross Ref Attitude estimation for ground vehicles using low-cost sensors with in-vehicle calibration Cross Ref Stereo Vision-Based Relative Position and Attitude Estimation of Non-Cooperative Spacecraft20 August 2021 | Aerospace, Vol. 8, No. 8 Cross Ref The package: nonparametric regression using local rotation matrices in8 April 2021 | Journal of Statistical Computation and Simulation, Vol. 91, No. 11 Cross Ref Multi-view subspace clustering with consistent and view-specific latent factors and coefficient matrices Cross Ref Lightweight Extended Kalman Filter for MARG Sensors Attitude EstimationIEEE Sensors Journal, Vol. 21, No. 13 Cross Ref Systematic Errors of Starry Sky Simulators Using Raster Screens12 January 2022 | Optoelectronics, Instrumentation and Data Processing, Vol. 57, No. 4 Cross Ref A Compressed and High-Accuracy Star Tracker with On-Orbit Deployable Baffle for Remote Sensing CubeSats26 June 2021 | Remote Sensing, Vol. 13, No. 13 Cross Ref Characterization of Degenerate Configurations in Attitude Determination of Three-Vehicle Heterogeneous Formations6 July 2021 | Sensors, Vol. 21, No. 14 Cross Ref Performance Enhancement of Consumer-Grade MEMS Sensors through Geometrical Redundancy16 July 2021 | Sensors, Vol. 21, No. 14 Cross Ref Attitude observers for three-vehicle heterogeneous formations based on the Lagrange-d’Alembert principle Cross Ref Estimation of Attitude Using Robust Adaptive Kalman Filter Cross Ref Recursive optimal linear attitude estimator based on star sensor and gyro22 March 2021 | Aerospace Systems, Vol. 4, No. 2 Cross Ref A geometric framework for rigid body attitude estimationAutomatica, Vol. 128 Cross Ref Anti-swaying self-alignment method based on observation vector inertia for SINS under latitude uncertaintyMeasurement, Vol. 177 Cross Ref Spatiotemporal Registration for Event-based Visual Odometry Cross Ref Coarse alignment of marine strapdown inertial navigation system using the location of fitted parametric circle of gravity movement5 March 2021 | Journal of Navigation, Vol. 74, No. 3 Cross Ref Spherical calibration and quality control of ground and UAV vector magnetometer dataThe Leading Edge, Vol. 40, No. 5 Cross Ref 40 years of sensor fusion for orientation tracking via magnetic and inertial measurement units: Methods, lessons learned, and future challengesInformation Fusion, Vol. 68 Cross Ref TEASER: Fast and Certifiable Point Cloud RegistrationIEEE Transactions on Robotics, Vol. 37, No. 2 Cross Ref Finite transformation rigid motion mesh morpher; A grid deformation approach7 October 2020 | International Journal for Numerical Methods in Fluids, Vol. 93, No. 3 Cross Ref Research on initial alignment method of vehicle-mounted SINS based on reverse navigationJournal of Physics: Conference Series, Vol. 1846, No. 1 Cross Ref Error Analysis of Accelerometer- and Magnetometer-Based Stationary Alignment14 March 2021 | Sensors, Vol. 21, No. 6 Cross Ref Spacecraft Attitude Determination4 August 2021 Cross Ref Kinematics9 December 2020 Cross Ref On Selection and Extraction of Biometric Features of Human Motor Activity from Data Obtained from Inertial Measurement Units16 July 2021 Cross Ref Conditional equivalence between Extended Kalman filter and complementary filter for two-vector gyro-aided attitude determinationMeasurement, Vol. 168 Cross Ref A Tutorial on Horizon-Based Optical Navigation and Attitude Determination With Space Imaging SystemsIEEE Access, Vol. 9 Cross Ref Star Identification and Attitude Determination With Projective CamerasIEEE Access, Vol. 9 Cross Ref Planning With AttitudeIEEE Robotics and Automation Letters Cross Ref The Fast Attitude Estimation Method Based on Quaternion and Generalized MultivectorsIEEE Transactions on Instrumentation and Measurement, Vol. 70 Cross Ref A Unified Method for Robust Self-Calibration of 3-D Field Sensor ArraysIEEE Transactions on Instrumentation and Measurement, Vol. 70 Cross Ref Attitude Estimation Method of High-Spinning Body Through Onboard Sensor Fusion Under Uniaxial Gyroscope Saturation EnvironmentIEEE Transactions on Instrumentation and Measurement, Vol. 70 Cross Ref Nonlinear Error Model Based on Quaternion for the INS: Analysis and ComparisonIEEE Transactions on Vehicular Technology, Vol. 70, No. 1 Cross Ref A systematic review of augmented reality tourism research: What is now and what is next?23 July 2020 | Tourism and Hospitality Research, Vol. 21, No. 1 Cross Ref Low-Rank Representation Algorithm Based on Latent Feature SpaceComputer Science and Application, Vol. 11, No. 04 Cross Ref Attitude Estimation with Albedo Interference on Sun Sensor MeasurementsJournal of Spacecraft and Rockets, Vol. 58, No. 1 Cross Ref Rigid Body Geometric Attitude Estimator using Multi-rate Sensors Cross Ref Attitude observers aided by implicit measurements of the Earth angular velocity Cross Ref Observers Design for Inertial Navigation Systems: A Brief Tutorial Cross Ref Quaternions as a solution to determining the angular kinematics of human movement23 March 2020 | BMC Biomedical Engineering, Vol. 2, No. 1 Cross Ref Applying Neural Networks in Aerial Vehicle Guidance to Simplify Navigation Systems11 December 2020 | Algorithms, Vol. 13, No. 12 Cross Ref Statistical Methods for Three-Axis Attitude Determination Cross Ref Attitude determination improvement in accelerated motions for maneuvering underwater vehiclesApplied Ocean Research, Vol. 104 Cross Ref Constrained Kalman filter for uncooperative spacecraft estimation by stereovisionAerospace Science and Technology, Vol. 106 Cross Ref A New Quaternion-Based Kalman Filter for Human Body Motion Tracking Using the Second Estimator of the Optimal Quaternion Algorithm and the Joint Angle Constraint Method with Inertial and Magnetic Sensors23 October 2020 | Sensors, Vol. 20, No. 21 Cross Ref MAV quaternion attitude determination for accelerometer-magnetometer combination: Internal analysis4 July 2020 | tm - Technisches Messen, Vol. 87, No. 10 Cross Ref Pose localization of leader–follower networks with direction measurementsAutomatica, Vol. 120 Cross Ref MARG Attitude Estimation Using Gradient-Descent Linear Kalman FilterIEEE Transactions on Automation Science and Engineering, Vol. 17, No. 4 Cross Ref In-Motion Alignment for Doppler Velocity Log-Aided SINS Based on Initial Velocity Error EstimationIEEE Transactions on Instrumentation and Measurement, Vol. 69, No. 10 Cross Ref Attitude Angles Determination by Vectors Observations in Airplane Free Spin Investigation19 February 2021 | Gyroscopy and Navigation, Vol. 11, No. 4 Cross Ref Does the Position of Foot-Mounted IMU Sensors Influence the Accuracy of Spatio-Temporal Parameters in Endurance Running?7 October 2020 | Sensors, Vol. 20, No. 19 Cross Ref Point-wise weighted solution for the similarity transformation parameters26 May 2020 | Applied Geomatics, Vol. 12, No. 3 Cross Ref CoBe - Coded Beacons for Localization, Object Tracking, and SLAM Augmentation Cross Ref Multi-view classifier based on Probabilistic Collaborative Representation and Latent Representation Cross Ref Adaptive Complementary Filtering Algorithm for IMU Based on MEMS Cross Ref TWOLATE: Total Registration of Point-Clouds Using a Weighted Optimal Linear Attitude and Translation Estimator Cross Ref A Wearable Magnetometer-Free Motion Capture System: Innovative Solutions for Real-World ApplicationsIEEE Sensors Journal, Vol. 20, No. 15 Cross Ref Limitation of Rayleigh sky model for bioinspired polarized skylight navigation in three-dimensional attitude determination19 May 2020 | Bioinspiration & Biomimetics, Vol. 15, No. 4 Cross Ref An Improved Algorithm for Universal Sensor Registration Cross Ref Fast AHRS Filter for Accelerometer, Magnetometer, and Gyroscope Combination with Separated Sensor Corrections9 July 2020 | Sensors, Vol. 20, No. 14 Cross Ref Special Cases in the Attitude Determination of Three-Vehicle Heterogeneous Formations Cross Ref In-Flight Calibration and Performance of the OSIRIS-REx Touch And Go Camera System (TAGCAMS)10 June 2020 | Space Science Reviews, Vol. 216, No. 4 Cross Ref Linear geometric algebra rotor estimator for efficient mesh deformation18 January 2021 | IET Cyber-Systems and Robotics, Vol. 2, No. 2 Cross Ref Novel Noniterative Orientation Estimation for Wearable Motion Sensor Units Acquiring Accelerometer, Gyroscope, and Magnetometer MeasurementsIEEE Transactions on Instrumentation and Measurement, Vol. 69, No. 6 Cross Ref Hand-Eye Calibration: 4-D Procrustes Analysis ApproachIEEE Transactions on Instrumentation and Measurement, Vol. 69, No. 6 Cross Ref Autonomous Toy Drone via Coresets for Pose Estimation27 May 2020 | Sensors, Vol. 20, No. 11 Cross Ref Flexibilities of wavelets as a computational basis set for large-scale electronic structure calculationsThe Journal of Chemical Physics, Vol. 152, No. 19 Cross Ref Matrix Method for Determining the Body Attitude14 November 2020 | International Applied Mechanics, Vol. 56, No. 3 Cross Ref A Conversation with Grace WahbaStatistical Science, Vol. 35, No. 2 Cross Ref Partially error-affected point-wise weighted closed-form solution to the similarity transformation and its variantsJournal of Applied Geodesy, Vol. 14, No. 2 Cross Ref Procrustes analysis for the virtual trial assembly of large-size elementsRobotics and Computer-Integrated Manufacturing, Vol. 62 Cross Ref A fast in-motion alignment based on inertial frame and reverse navigation Cross Ref Deeply Integrated GNSS/Gyro Attitude Determination System13 April 2020 | Sensors, Vol. 20, No. 8 Cross Ref Optimal Linear Orbit DeterminationJournal of Guidance, Control, and Dynamics, Vol. 43, No. 3 Cross Ref A Novel GNSS Attitude Determination Method Based on Primary Baseline Switching for A Multi-Antenna Platform25 February 2020 | Remote Sensing, Vol. 12, No. 5 Cross Ref Kalman Filter Cascade for Attitude Estimation on Rotating EarthIEEE/ASME Transactions on Mechatronics, Vol. 25, No. 1 Cross Ref A Novel Fuzzy-Adaptive Extended Kalman Filter for Real-Time Attitude Estimation of Mobile Robots1 February 2020 | Sensors, Vol. 20, No. 3 Cross Ref A linear computationally efficient Kalman filter for robust attitude estimation from horizon measurements and GNSS observationsSensor Review, Vol. 40, No. 2 Cross Ref A Simplified Method to Determine Gravity Vector Through Aerodynamic Coefficients and its Applications in Attitude Determination18 April 2019 Cross Ref Enhancing the Flexibility of First Principles Simulations of Materials via Wavelets14 February 2020 Cross Ref A Constrained Kalman Filter for Rigid Body Systems with Frictional Contact8 May 2020 Cross Ref Practical Exponential Coordinates Using Implicit Dual Quaternions8 May 2020 Cross Ref Morphological Modelling and Simulation of Crystallization Processes21 June 2020 Cross Ref LEO satellite active FTC with aerodynamic disturbance decoupled fault diagnosisEuropean Journal of Control, Vol. 51 Cross Ref An accuracy of better than 200 m in positioning using a portable star trackerNew Astronomy, Vol. 74 Cross Ref Hybrid RRT: A Semi-dual-tree RRT-based Motion PlannerIEEE Access Cross Ref Informed RRT*-Connect: An Asymptotically Optimal Single-Query Path Planning MethodIEEE Access, Vol. 8 Cross Ref GNSS-Based Attitude Determination Techniques—A Comprehensive Literature SurveyIEEE Access, Vol. 8 Cross Ref Relative Pose Estimation Based on With to Access, Vol. 8 Cross Ref Rigid 3D A Method Free of and Transactions on Instrumentation and Measurement Cross Ref Generalized Latent Transactions on Analysis and Intelligence, Vol. No. 1 Cross Ref of Spacecraft and Rockets, Vol. 57, No. 1 Cross Ref A Attitude Determination for Small Design of the Algorithm and January 2020 | Aerospace, Vol. 7, No. 1 Cross Ref Attitude Sensor from A Numerical and January 2020 | Sensors, Vol. 20, No. 2 Cross Ref A New In-Flight Alignment Method with an to the Low-Cost Integrated Navigation January 2020 | Sensors, Vol. 20, No. 2 Cross Ref A Observer for Relative Attitude Estimation Cross Ref Observer and filter based attitude estimation for rigid to Cross Ref Attitude Fusion Based on EKF for Cross Ref Attitude estimation using Engineering Practice, Vol. Cross Ref A Fast and Robust Algorithm for Orientation Estimation Using Inertial Letters, Vol. No. 11 Cross Ref A solution for the attitude determination of three-vehicle heterogeneous Science and Technology, Vol. Cross Ref Fast orthogonal networks a for orthogonal Processing, Vol. Cross Ref An Improved Algorithm for Intelligent Cross Ref A Quaternion-Based Optimal to the With Cross Ref Human and Inertial Measurements to Quaternion-Based September 2019 | Sensors, Vol. 19, No. 19 Cross Ref A robust and fast self-alignment method for strapdown inertial navigation system in Engineering, Vol. Cross Ref Attitude Filtering with and Measurement Covariance of Aerospace Engineering, Vol. 32, No. 5 Cross Ref Gradient Descent Optimization-Based Method for Stationary Transactions on Instrumentation and Measurement, Vol. 68, No. 9 Cross Ref Nonlinear Attitude on the Special and Transactions on Systems, and Systems, Vol. No. 9 Cross Ref Constrained Attitude Determination from Vector and September 2019 | Aerospace, Vol. No. 9 Cross Ref for extended from April 2019 | Journal of Physics: Vol. No. Cross Ref Direct and Transactions on Vol. 38, No. 4 Cross Ref EKF attitude estimation with measurement November | Journal of Control, Vol. 21, No. 4 Cross Ref stable attitude with Earth velocity March 2019 | Journal of Control, Vol. 21, No. 4 Cross Ref Finite stable attitude estimation of rigid with April 2019 | Journal of Control, Vol. 21, No. 4 Cross Ref observation to attitude estimation in Space Research, Vol. No. 1 Cross Ref Calibration Using Estimation Approach Cross Ref Generalized Linear Quaternion Complementary Filter for Attitude Estimation An Optimization ApproachIEEE Transactions on Automation Science and Engineering, Vol. 16, No. 3 Cross Ref the Scheme of Initial Attitude Estimation Using Low Accuracy December 2019 | Vol. No. 3 Cross Ref Finite Attitude and Angular Velocity Estimation for Rigid With Cross Ref Sensing and Estimation of Spacecraft Cross Ref Nonlinear and attitude filter on the Special of the Vol. No. Cross Ref Study the of star sensor by of sensor Cross Ref GNSS Integrated With MEMS for and Attitude Determination in Sensors Journal, Vol. 19, No. 9 Cross Ref Attitude determination sensor for Earth satellite based on May | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. No. 6 Cross Ref and Robust and Scheme Using Weighted Least Journal, Vol. 57, No. 5 Cross Ref Attitude on the orthogonal with Earth velocity & Control Letters, Vol. Cross Ref Analysis of Optimization of Attitude Determination from Vector Observations Cross Ref Nonlinear Observer on for Attitude Estimation on Rotating Earth Using Vector MeasurementsIEEE Control Systems Letters, Vol. No. 2 Cross Ref A on the Computation of Quaternions Rotation March 2019 | Journal of and Robotics, Vol. 11, No. 2 Cross Ref of the Method of for Determining the Orientation of a Body in April 2019 | Automation and Remote Control, Vol. No. 4 Cross Ref Generalized Attitude Determination with Vector of Guidance, Control, and Dynamics, Vol. No. 4 Cross Ref of GNSS detection based on for December | Space Journal, Vol. 11, No. 1 Cross Ref A solution to the navigation satellite system attitude determination December | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. No. 3 Cross Ref magnetic disturbance determination for vehicles via gravity and navigation satellite system January 2019 | Measurement Science and Technology, Vol. No. 2 Cross Ref attitude with inertial measurement and applications of GNSS to the January 2019 | Measurement Science and Technology, Vol. No. 2 Cross Ref Kalman Filtering for Estimation of Attitude and Gyroscope Transactions on Mechatronics, Vol. 24, No. 1 Cross Ref Estimation for Attitude and Systems Under Sensors Journal, Vol. 19, No. 2 Cross Ref A Total Estimate for Attitude Determination6 January 2019 Cross Ref Analysis of the Total Least Squares with January 2019 Cross Ref for July | Journal of the Statistical Vol. No. Cross Ref Spacecraft Attitude October 2019 Cross Ref Procrustes March 2019 Cross Ref Procrustes March 2019 Cross Ref 3D Using Quaternions for Orientation and in September 2019 Cross Ref Adaptive Attitude Determination Method Using Low-Cost MARG Sensors23 November 2019 Cross Ref Finite Rigid Motion September Cross Ref Improved attitude determination by of by of and Vol. Cross Ref A Factor Approach for Attitude Estimation of Spacecraft Using a Stellar Access, Vol. Cross Ref In-Motion Attitude and Position Alignment for SINS Based on Backtracking Access, Vol. Cross Ref Pose Estimation for Ground Transactions on Automation Science and Engineering, Vol. 16, No. 1 Cross Ref Spacecraft attitude estimation based on matrix Kalman filter and recursive Kalman August | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. No. Cross Ref attitude determination February | International Journal of Vol. No. 4 Cross Ref in models using rigid body transformation estimation and February | in Engineering, Vol. No. 1 Cross Ref Simplified Attitude Determination Algorithm Using and Magnetometer with Low of Sensors,

Previous article Next article Bounds on Multiprocessing Timing AnomaliesR. L. GrahamR. L. Grahamhttps://doi.org/10.1137/0117039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. F. Codd, Multiprogram scheduling. I, II. Introduction and theory, Comm. ACM, 3 (1960), 347–350 10.1145/367297.367317 MR0130079 0102.34202 CrossrefISIGoogle Scholar[2] R. L. Graham, Bounds for certain multiprocessing anomalies, Bell System Tech. J., 45 (1966), 1563–1581 0168.40703 CrossrefISIGoogle Scholar[3] J. Heller, Sequencing aspects of multiprogramming, J. Assoc. Comput. Mach., 8 (1961), 426–439 MR0159443 CrossrefGoogle Scholar[4] John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955xiv+298 MR0070144 0066.16604 Google Scholar[5] B. Liebesman, The use of a special algebra in schedule analysis, to appear Google Scholar[6] G. K. Manacher, Production and stabilization of real-time task schedules, J. Assoc. Comput. Mach., 14 (1967), 439–465 CrossrefISIGoogle Scholar[7] B. P. Ochsner, Controlling a multiprocessor system, Record, 44, Bell Laboratories, 1966, pp. 59–62 Google Scholar[8] P. Richards, Parallel programming, Rep., TD-B60-27, Technical Operations Inc., 1960 Google Scholar[9] M. Rothkopf, Scheduling independent tasks on one or more processors, Interim Tech. Rep., 2, Operations Research Center, M.I.T., Cambridge, 1964 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails DAG Scheduling and Analysis on Multi-Core Systems by Modelling Parallelism and DependencyIEEE Transactions on Parallel and Distributed Systems, Vol. 33, No. 12 | 1 Dec 2022 Cross Ref The BH-mixed scheduling algorithm for DAG tasks with constrained deadlinesJournal of Systems Architecture, Vol. 131 | 1 Oct 2022 Cross Ref Streaming algorithms for multitasking scheduling with shared processingDiscrete Applied Mathematics, Vol. 320 | 1 Oct 2022 Cross Ref Checkpointing Workflows à la Young/Daly Is Not Good EnoughACM Transactions on Parallel Computing, Vol. 25 | 2 September 2022 Cross Ref Parallel Machine Scheduling Under Uncertainty: Models and Exact AlgorithmsINFORMS Journal on Computing, Vol. 68 | 17 August 2022 Cross Ref EasyFL: A Low-Code Federated Learning Platform for DummiesIEEE Internet of Things Journal, Vol. 9, No. 15 | 1 Aug 2022 Cross Ref Demand-Aware Network Design With Minimal Congestion and Route LengthsIEEE/ACM Transactions on Networking, Vol. 30, No. 4 | 1 Aug 2022 Cross Ref Speed scaling scheduling of multiprocessor jobs with energy constraint and makespan criterionJournal of Global Optimization, Vol. 83, No. 3 | 26 November 2021 Cross Ref An Efficient Parallel Algorithm for Detecting Packet Filter ConflictsAlgorithms, Vol. 15, No. 7 | 7 July 2022 Cross Ref A two-stage genetic programming framework for Stochastic Resource Constrained Multi-Project Scheduling Problem under New Project InsertionsApplied Soft Computing, Vol. 124 | 1 Jul 2022 Cross Ref Minimizing makespan on parallel batch processing machines with two-dimensional rectangular jobsComputers & Industrial Engineering, Vol. 169 | 1 Jul 2022 Cross Ref Joinable Parallel Balanced Binary TreesACM Transactions on Parallel Computing, Vol. 9, No. 2 | 30 Jun 2022 Cross Ref Work-conserving disciplines are asymptotic optimal in completion time minimizationIISE Transactions, Vol. 43 | 30 June 2022 Cross Ref Tight approximation bounds for the LPT rule applied to identical parallel machines with small jobsJournal of Scheduling, Vol. 1 | 28 June 2022 Cross Ref A novel genetic algorithm based system for the scheduling of medical treatmentsExpert Systems with Applications, Vol. 195 | 1 Jun 2022 Cross Ref Bounding the execution time of parallel applications on unrelated multiprocessorsReal-Time Systems, Vol. 58, No. 2 | 21 October 2021 Cross Ref Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion timeEuropean Journal of Operational Research, Vol. 52 | 1 Jun 2022 Cross Ref The fellowship of the Dyson ring: ACT&Friends’ results and methods for GTOC 11Acta Astronautica, Vol. 8 | 1 Jun 2022 Cross Ref Efficient Simulation of 3D Reaction-Diffusion in Models of Neurons and NetworksFrontiers in Neuroinformatics, Vol. 16 | 17 May 2022 Cross Ref Malleable scheduling beyond identical machinesJournal of Scheduling, Vol. 12 | 11 May 2022 Cross Ref Faster Minimization of Tardy Processing Time on a Single MachineAlgorithmica, Vol. 84, No. 5 | 27 January 2022 Cross Ref Guaranteeing Safety Despite Physical Errors in Cyber-Physical Systems2022 IEEE 28th Real-Time and Embedded Technology and Applications Symposium (RTAS) | 1 May 2022 Cross Ref Minimizing DAG Utilization by Exploiting SMT2022 IEEE 28th Real-Time and Embedded Technology and Applications Symposium (RTAS) | 1 May 2022 Cross Ref Response time analysis of parallel tasks on accelerator-based heterogeneous platformsJournal of Systems Architecture, Vol. 126 | 1 May 2022 Cross Ref Out-of-Core Edge Partitioning at Linear Run-Time2022 IEEE 38th International Conference on Data Engineering (ICDE) | 1 May 2022 Cross Ref Variable neighbourhood search for job scheduling with position-dependent deteriorating processing timesJournal of the Operational Research Society, Vol. 131 | 26 April 2022 Cross Ref On the Evaluation of the Ambulance Capacity of the Asian Side of Istanbul in the Case of a Serious EarthquakeDisaster Medicine and Public Health Preparedness, Vol. 16, No. 2 | 27 October 2020 Cross Ref An adaptive self‐scheduling loop schedulerConcurrency and Computation: Practice and Experience, Vol. 34, No. 6 | 2 December 2021 Cross Ref Semi-online scheduling: A surveyComputers & Operations Research, Vol. 139 | 1 Mar 2022 Cross Ref Multi-station test scheduling optimization method for industrial robot servo systemJournal of Ambient Intelligence and Humanized Computing, Vol. 13, No. 3 | 15 October 2020 Cross Ref Computing exact WCRT for typed DAG tasks on heterogeneous multi-core processorsJournal of Systems Architecture, Vol. 124 | 1 Mar 2022 Cross Ref Effects of Continuous vs Discrete Frequency Scaling and Core Allocation on Energy Efficiency of Static Schedules for Moldable TasksParallel Processing Letters, Vol. 32, No. 01n02 | 10 December 2021 Cross Ref Single-machine scheduling with machine unavailability periods and resource dependent processing timesEuropean Journal of Operational Research, Vol. 296, No. 2 | 1 Jan 2022 Cross Ref The Piggyback Transportation Problem: Transporting drones launched from a flying warehouseEuropean Journal of Operational Research, Vol. 296, No. 2 | 1 Jan 2022 Cross Ref A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular PenaltiesMathematics, Vol. 10, No. 1 | 25 December 2021 Cross Ref Scheduling of Real-Time Tasks With Multiple Critical Sections in Multiprocessor SystemsIEEE Transactions on Computers, Vol. 71, No. 1 | 1 Jan 2022 Cross Ref Noncooperative Supply Chain SchedulingSupply Chain Scheduling | 20 October 2021 Cross Ref Saving power in disks, flash memories, and serversStorage Systems | 1 Jan 2022 Cross Ref BibliographyStorage Systems | 1 Jan 2022 Cross Ref A 2-Competitive Largest Job on Least Loaded Machine Online Algorithm Based on the Multi List Scheduling ModelProceedings of the Seventh International Conference on Mathematics and Computing | 6 March 2022 Cross Ref New Results on Competitive Analysis of Online SRPT SchedulingProceedings of the Seventh International Conference on Mathematics and Computing | 6 March 2022 Cross Ref Scheduling K-mers Counting in a Distributed EnvironmentOptimization in Artificial Intelligence and Data Sciences | 2 March 2022 Cross Ref A Parallel Algorithm for GAC Filtering of the Alldifferent ConstraintIntegration of Constraint Programming, Artificial Intelligence, and Operations Research | 10 June 2022 Cross Ref Exploring Scheduling Algorithms for Parallel Task Graphs: A Modern Game Engine Case StudyEuro-Par 2022: Parallel Processing | 1 August 2022 Cross Ref Approximation Schemes for Machine SchedulingOperations Research Proceedings 2021 | 30 August 2022 Cross Ref Approximation Scheme for Single-Machine Rescheduling with Job Delay and RejectionAlgorithmic Aspects in Information and Management | 18 September 2022 Cross Ref The Constrained Parallel-Machine Scheduling Problem with Divisible Processing Times and PenaltiesAlgorithmic Aspects in Information and Management | 18 September 2022 Cross Ref PathTracer: Understanding Response Time of Signal Processing Applications on Heterogeneous MPSoCsACM Transactions on Modeling and Performance Evaluation of Computing Systems, Vol. 6, No. 4 | 31 Dec 2021 Cross Ref Energy-efficient scheduling: classification, bounds, and algorithmsSādhanā, Vol. 46, No. 1 | 26 February 2021 Cross Ref A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operatorsFlexible Services and Manufacturing Journal, Vol. 33, No. 4 | 28 November 2020 Cross Ref Improved scalability of demand-aware datacenter topologies with minimal route lengths and congestionPerformance Evaluation, Vol. 152 | 1 Dec 2021 Cross Ref Online Makespan Scheduling with Job Migration on Uniform MachinesAlgorithmica, Vol. 83, No. 12 | 19 August 2021 Cross Ref Opportunistic Overlapping: Joint scheduling of uplink URLLC/eMBB traffic in NOMA based Wireless Systems2021 19th International Symposium on Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt) | 18 Oct 2021 Cross Ref A note on labeling methods to schedule unit execution time tasks in the presence of delayed precedence constraintsJournal of Parallel and Distributed Computing, Vol. 156 | 1 Oct 2021 Cross Ref Bounding schemes for the parallel machine scheduling problem with DeJong's learning effectJournal of Parallel and Distributed Computing, Vol. 156 | 1 Oct 2021 Cross Ref Mixed-Cell-Height Detailed Placement Considering Complex Minimum-Implant-Area ConstraintsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 40, No. 10 | 1 Oct 2021 Cross Ref Simulation-based priority rules for the stochastic resource-constrained net present value and risk problemComputers & Industrial Engineering, Vol. 160 | 1 Oct 2021 Cross Ref Cost-adaptive multi-class multicast service aggregation based on distributed sub-trees in elastic optical data center networksOptical Fiber Technology, Vol. 66 | 1 Oct 2021 Cross Ref Delay and Cost Optimization in Computational Offloading Systems with Unknown Task Processing TimesIEEE Transactions on Cloud Computing, Vol. 9, No. 4 | 1 Oct 2021 Cross Ref Lap: A latency‐aware parallelism framework for content‐based publish/subscribe systemsConcurrency and Computation: Practice and Experience, Vol. 35 | 21 September 2021 Cross Ref Improved co-scheduling of multi-layer printing path scanning for collaborative additive manufacturingIISE Transactions, Vol. 53, No. 9 | 17 September 2020 Cross Ref Approximation algorithms for makespan minimization on identical parallel machines under resource constraintsJournal of the Operational Research Society, Vol. 72, No. 9 | 23 June 2020 Cross Ref Best Fit Bin Packing with Random Order RevisitedAlgorithmica, Vol. 83, No. 9 | 1 July 2021 Cross Ref Approximation algorithms for the multiprocessor scheduling with submodular penaltiesOptimization Letters, Vol. 15, No. 6 | 20 March 2021 Cross Ref An improved parametric algorithm on two-machine scheduling with given lower and upper bounds for the total processing timeTheoretical Computer Science, Vol. 880 | 1 Aug 2021 Cross Ref Greedy is Optimal for Online Restricted Assignment and Smart Grid Scheduling for Unit Size JobsTheory of Computing Systems, Vol. 65, No. 6 | 8 April 2021 Cross Ref Single Machine Vector Scheduling with General PenaltiesMathematics, Vol. 9, No. 16 | 17 August 2021 Cross Ref A Survey on Problem Formulations and (Meta)Heuristic-Based Solutions in Automated Assembly of Parallel Test FormsInternational Journal of Software Engineering and Knowledge Engineering, Vol. 31, No. 08 | 14 September 2021 Cross Ref Timing-Anomaly Free Dynamic Scheduling of Periodic DAG Tasks with Non-Preemptive Nodes2021 IEEE 27th International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA) | 1 Aug 2021 Cross Ref Graph-Based Optimizations for Multiprocessor Nested Resource Sharing2021 IEEE 27th International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA) | 1 Aug 2021 Cross Ref Greedy Successive Relaying for the Multicarrier Diamond Relay Channel2021 National Conference on Communications (NCC) | 27 Jul 2021 Cross Ref Buffer minimization with conflicts on a lineTheoretical Computer Science, Vol. 876 | 1 Jul 2021 Cross Ref ARTful: A model for user‐defined schedulers targeting multiple high‐performance computing runtime systemsSoftware: Practice and Experience, Vol. 51, No. 7 | 4 April 2021 Cross Ref In-Memory Interval JoinsThe VLDB Journal, Vol. 30, No. 4 | 8 April 2021 Cross Ref Efficient Pre-Solve Algorithms for the Schwerin and Falkenauer_U Bin Packing Benchmark Problems for Getting Optimal Solutions with High ProbabilityMathematics, Vol. 9, No. 13 | 1 July 2021 Cross Ref Teaching Complex Scheduling Algorithms2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) | 1 Jun 2021 Cross Ref Makespan minimization with OR-precedence constraintsJournal of Scheduling, Vol. 24, No. 3 | 29 May 2021 Cross Ref Implementing synchronous reactive components upon multiprocessor platformsJournal of Systems Architecture, Vol. 116 | 1 Jun 2021 Cross Ref Offline preemptive bottom left decreasing height scheduling of power loads in smart gridsEnergy Systems, Vol. 9 | 31 May 2021 Cross Ref Disruption-Free Load Balancing for Aerial Access NetworkWireless Communications and Mobile Computing, Vol. 2021 | 23 May 2021 Cross Ref K‐ear: Extracting data access periodic characteristics for energy‐aware data clustering and storing in cloud storage systemsConcurrency and Computation: Practice and Experience, Vol. 33, No. 9 | 30 November 2020 Cross Ref Absolute bounds of list algorithms for parallel machines scheduling with unavailability periodsInternational Transactions in Operational Research, Vol. 28, No. 3 | 30 August 2018 Cross Ref Argus: Efficient Job Scheduling in RDMA-assisted Big Data Processing2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2021 Cross Ref Iterative job splitting algorithms for parallel machine scheduling with job splitting and setup resource constraintsJournal of the Operational Research Society, Vol. 72, No. 4 | 6 February 2020 Cross Ref Ideal schedules in parallel machine settingsEuropean Journal of Operational Research, Vol. 290, No. 2 | 1 Apr 2021 Cross Ref Exact lexicographic scheduling and approximate reschedulingEuropean Journal of Operational Research, Vol. 290, No. 2 | 1 Apr 2021 Cross Ref Approximate and robust bounded job start scheduling for Royal Mail delivery officesJournal of Scheduling, Vol. 24, No. 2 | 21 March 2021 Cross Ref Two-Aggregator Topology Optimization Using Single Paths in Data Center NetworksIEEE Transactions on Cloud Computing, Vol. 9, No. 2 | 1 Apr 2021 Cross Ref Continuously Bulk Loading over Range Partitioned Tables for Large Scale Historical Data2021 IEEE 37th International Conference on Data Engineering (ICDE) | 1 Apr 2021 Cross Ref Automatic detection of the best performing priority rule for the resource-constrained project scheduling problemExpert Systems with Applications, Vol. 167 | 1 Apr 2021 Cross Ref A hyper-heuristic based ensemble genetic programming approach for stochastic resource constrained project scheduling problemExpert Systems with Applications, Vol. 167 | 1 Apr 2021 Cross Ref Relative Worst-order AnalysisACM Computing Surveys, Vol. 54, No. 1 | 1 Apr 2021 Cross Ref A mixed-integer linear programming model to solve the Multidimensional Multi-Way Number Partitioning ProblemComputers & Operations Research, Vol. 127 | 1 Mar 2021 Cross Ref Capacity Approaching Low Density Spreading in Uplink NOMA via Asymptotic AnalysisIEEE Transactions on Communications, Vol. 69, No. 3 | 1 Mar 2021 Cross Ref Maximin share guarantee for goods with positive externalitiesSocial Choice and Welfare, Vol. 56, No. 2 | 27 August 2020 Cross Ref Scheduling uniform parallel dedicated machines with job splitting, sequence-dependent setup times, and multiple serversComputers & Operations Research, Vol. 126 | 1 Feb 2021 Cross Ref Efficient Hybrid Density Functional Calculations for Large Periodic Systems Using Numerical Atomic OrbitalsJournal of Chemical Theory and Computation, Vol. 17, No. 1 | 14 December 2020 Cross Ref Mixed coordination mechanisms for scheduling games on hierarchical machinesInternational Transactions in Operational Research, Vol. 28, No. 1 | 25 May 2018 Cross Ref Integrated Scheduling of Tasks and Preventive Maintenance Periods in a Parallel Machine Environment With Single Robot ServerIEEE Access, Vol. 9 | 1 Jan 2021 Cross Ref Scheduling ortsfester GebrauchsfaktorenProduktionstheorie 4 | 17 May 2021 Cross Ref Schedule Explainer: An Argumentation-Supported Tool for Interactive Explanations in Makespan SchedulingExplainable and Transparent AI and Multi-Agent Systems | 17 July 2021 Cross Ref Update on the Asymptotic Optimality of LPTEuro-Par 2021: Parallel Processing | 25 August 2021 Cross Ref A Log-Linear $$(2 +5/6)$$-Approximation Algorithm for Parallel Machine Scheduling with a Single Orthogonal ResourceEuro-Par 2021: Parallel Processing | 25 August 2021 Cross Ref Scheduling with Testing on Multiple Identical Parallel MachinesAlgorithms and Data Structures | 31 July 2021 Cross Ref A Fluid Scheduling Algorithm for DAG Tasks with Constrained or Arbitrary DeadlinesIEEE Transactions on Computers | 1 Jan 2021 Cross Ref Improved MapReduce Load Balancing through Distribution-Dependent Hash Function Optimization2020 IEEE 26th International Conference on Parallel and Distributed Systems (ICPADS) | 1 Dec 2020 Cross Ref An exact algorithm for identical parallel machine scheduling under scenarios2020 3rd World Conference on Mechanical Engineering and Intelligent Manufacturing (WCMEIM) | 1 Dec 2020 Cross Ref Vector scheduling with rejection on two machinesInternational Journal of Computer Mathematics, Vol. 97, No. 12 | 9 January 2020 Cross Ref Anomalies in Special Permutation Flow Shop Scheduling ProblemsChinese Journal of Mechanical Engineering, Vol. 33, No. 1 | 9 June 2020 Cross Ref DAG Scheduling and Analysis on Multiprocessor Systems: Exploitation of Parallelism and Dependency2020 IEEE Real-Time Systems Symposium (RTSS) | 1 Dec 2020 Cross Ref High-performance computing under availability constraints to solve dense triangular system2020 5th International Conference on Cloud Computing and Artificial Intelligence: Technologies and Applications (CloudTech) | 24 Nov 2020 Cross Ref Adversarial Attacks in a Deep Reinforcement Learning based Cluster Scheduler2020 28th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS) | 17 Nov 2020 Cross Ref Fast load balance parallel graph analytics with an automatic graph data structure selection algorithmFuture Generation Computer Systems, Vol. 112 | 1 Nov 2020 Cross Ref Influential nodes selection to enhance data dissemination in A of Network and Computer Applications, Vol. 169 | 1 Nov 2020 Cross Ref Scheduling jobs with and delivery on identical parallel batch Computer Science, Vol. | 1 Nov 2020 Cross Ref A of optimal multiprocessor schedules and of Combinatorial Optimization, Vol. 40, No. 4 | 12 August 2020 Cross Ref Scheduling on with IEEE Symposium on of Computer | 1 Nov 2020 Cross Ref the for Makespan Scheduling via of Operations Research, Vol. No. 4 | 1 Nov 2020 Cross Ref Parallel of with Parallel for IEEE International Conference on Systems, and | 11 Oct 2020 Cross Ref A approximation framework for and resource Journal of Operational Research, Vol. No. 1 | 1 Oct 2020 Cross Ref Approximation Algorithms for the Submodular Load Balancing with Submodular PenaltiesMathematics, Vol. No. 10 | 15 October 2020 Cross Ref Real-Time Scheduling and Analysis of DAG Tasks Nested Transactions on Computers, Vol. 69, No. 9 | 1 2020 Cross Ref Efficient Federated Scheduling for Parallel Real-Time IEEE 26th International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA) | 1 Aug 2020 Cross Ref On the Asymptotic Optimality of in Time International Conference on Computer Communications and Networks | 1 Aug 2020 Cross Ref Approximation for Scheduling on Parallel with or Problems New Applications and | 8 July 2020 Cross Ref Research on and for the of Job Shop Scheduling Problems in Engineering, Vol. 2020 | 6 Jul 2020 Cross Ref Scheduling on of Computing Surveys, Vol. 53, No. 3 | 5 Jul 2020 Cross Ref Scheduling for the Algorithms and IEEE Symposium on Computers and Communications | 1 Jul 2020 Cross Ref Scheduling MapReduce on Identical and of Computing Systems, Vol. No. 5 | 29 November Cross Ref Optimal scheduling of parallel real-time Systems, Vol. 56, No. 3 | 29 March 2020 Cross Ref On of Transactions on the Vol. No. 3 | 21 Jun 2020 Cross Ref Exact and heuristic algorithms for scheduling on two identical machines with & Industrial Engineering, Vol. | 1 Jun 2020 Cross Ref A genetic algorithm for Management Science, Vol. No. 2 | 27 March Cross Ref Resource Allocation in Low Density Spreading Uplink NOMA via Asymptotic IEEE International Symposium on Information Theory | 1 Jun 2020 Cross Ref Dynamic with Minimal of the on and Analysis of Computing Systems, Vol. No. 1 | 27 May 2020 Cross Ref On scheduling multiple two-stage Computer Science, Vol. | 1 May 2020 Cross Ref Real-Time scheduling and analysis of parallel tasks on heterogeneous of Systems Architecture, Vol. | 1 May 2020 Cross Ref for to for Packing in Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. No. 5 | 1 May 2020 Cross Ref The Efficient Multiprocessor of IEEE International Symposium on Real-Time Distributed Computing | 1 May 2020 Cross Ref Data Services for High Energy International Symposium on Cloud and Internet Computing | 1 May 2020 Cross Ref Analysis of a List Scheduling Algorithm for Task on of IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2020 Cross Ref On the of DAG Scheduling in Multiprocessor IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2020 Cross Ref Joint Task Scheduling and Management in IEEE International Parallel and Distributed Processing Symposium (IPDPS) | 1 May 2020 Cross Ref Machine scheduling with precedence Journal of Operational Research, Vol. No. 2 | 1 Apr 2020 Cross Ref of Parallel and Distributed Computing, Vol. | 1 Apr 2020 Cross Ref The Processing Time rule for identical parallel machines of Scheduling, Vol. No. 2 | 18 December 2018 Cross Ref of for task on machinesJournal of Combinatorial Optimization, Vol. | 6 March 2020 Cross Ref Transactions on Vol. 16, No. 1 | 5 Mar 2020 Cross Ref Improved approximation algorithms for two-stage scheduling Computer Science, Vol. | 1 Feb 2020 Cross Ref for Mixed Vol. No. 1 | 15 May Cross Ref A of of scheduling: and of Scheduling, Vol. No. 1 | 28 January 2020 Cross Ref A for Proceedings in Computer Science, Vol. | 20 January 2020 Cross Ref Makespan for Software Testing Under in of Computer Systems and Networks | 12 May Cross Ref Approximation algorithms for & Chemical Engineering, Vol. | 1 Jan 2020 Cross Ref Single with Time for Parallel Task Processing with and Unknown Transactions on Parallel and Distributed Systems, Vol. 31, No. 1 | 1 Jan 2020 Cross Ref An Approximation Algorithm for a Task Sequencing and Scheduling Problem a and | 1 Jan 2020 Cross Ref Greedy Is Optimal for Online Restricted Assignment and Smart Grid Scheduling for Unit Size and Online Algorithms | 25 January 2020 Cross Ref A Parallel Tool for the Simulation and Processing and Applied Mathematics | 19 March 2020 Cross Ref Makespan Minimization for Parallel with Energy Optimization Theory and Operations Research | 29 June 2020 Cross Ref Scheduling to Time via Linear Journal on Computing, Vol. No. 4 | 9 April on Hybrid Improved | 3 December 2020 Cross Ref An of a in Multiple Parallelism on Modern Systems | 1 September 2020 Cross Ref Buffer Minimization with on a in | 23 September 2020 Cross Ref Automated Journal of Vol. 24 | 17 Dec Cross Ref Scheduling of Performance Evaluation Vol. No. 2 | 4 Dec Cross Ref Uniform Parallel Machine Scheduling with Job and Vol. No. 24 | 13 December Cross Ref Modeling and Scheduling Problem with Uniform Parallel to Vol. No. 12 | 21 November Cross Ref Real-Time Scheduling of DAG Tasks with Arbitrary Transactions on Design of Systems, Vol. 24, No. 6 | 14 Nov Cross Ref Scheduling parallel identical machines to parallel approximation of Parallel and Distributed Computing, Vol. | 1 Nov Cross Ref scheduling of independent parallel tasks on and multiple processorsJournal of Parallel and Distributed Computing, Vol. | 1 Nov Cross Ref Minimizing machine over of the scheduling problem Computer Science, Vol. | 1 Nov Cross Ref Performance Tasks with for Cloud Data Center Resource Transactions on Parallel and Distributed Systems, Vol. 30, No. 11 | 1 Nov Cross Ref Response Time Bounds for DAG Parallel Tasks on Heterogeneous Transactions on Parallel and Distributed Systems, Vol. 30, No. 11 | 1 Nov Cross Ref The of and for Network of Operations Research, Vol. 44, No. 4 | 1 Nov Cross Ref Timing-Anomaly Free Dynamic Scheduling of DAG Tasks on Multi-Core Transactions on Embedded Computing Systems, Vol. No. | 19 Oct Cross Ref Two-Aggregator Topology Optimization Using Multiple Paths in Data Center NetworksIEEE Transactions on Cloud Computing, Vol. No. 4 | 1 Oct Cross Ref A of parallel machine scheduling with processing of Scheduling, Vol. No. 5 | 25 March Cross Ref on an of Computer Science, Vol. 13, No. 5 | 17 June Cross Ref On for with of the VLDB Vol. 13, No. 2 | 1 Oct Cross Ref Assignment in Real-Time Scheduling of DAG Tasks on Transactions on Parallel and Distributed Systems, Vol. 30, No. 10 | 1 Oct Cross Ref A of the loop schedulerConcurrency and Computation: Practice and Experience, Vol. 31, No. 18 | 1

Previous article Next article Convergence Conditions for Ascent MethodsPhilip WolfePhilip Wolfehttps://doi.org/10.1137/1011036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractLiberal conditions on the steps of a “descent” method for finding extrema of a function are given; most known results are special cases.[1] Haskell B. Curry, The method of steepest descent for non-linear minimization problems, Quart. Appl. Math., 2 (1944), 258–261 MR0010667 0061.26801 CrossrefGoogle Scholar[2] Augustine Cauchy, Méthode générale pour la résolution des systèmes d'équations simultanées, C.R. Acad. Sci., 25 (1847), 536–538 Google Scholar[3] A. A. Goldstein, Minimizing functionals on normed-linear spaces, SIAM J. Control, 4 (1966), 81–89 10.1137/0304008 MR0196900 0147.12701 LinkGoogle Scholar[4] A. A. Goldstein, Cauchy's method of minimization, Numer. Math., 4 (1962), 146–150 10.1007/BF01386306 MR0141222 0105.10201 CrossrefGoogle Scholar[5] Alexander Ostrowski, Solution of equations and systems of equations, Second edition. Pure and Applied Mathematics, Vol. 9, Academic Press, New York, 1966xiv+338 MR0216746 0222.65070 Google Scholar[6] G. Zoutehdijk, 1967, Private communication Google Scholar[7] R. Fletcher and , C. M. Reeves, Function minimization by conjugate gradients, Comput. J., 7 (1964), 149–154 10.1093/comjnl/7.2.149 MR0187375 0132.11701 CrossrefISIGoogle Scholar[8] W. Oettli, 1967, Private communication Google Scholar[9] L. V. Kantorovich and , G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964xiii+771, Chap. 15 MR0213845 0127.06104 Google Scholar[10] Hirotugu Akaike, On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method, Ann. Inst. Statist. Math. Tokyo, 11 (1959), 1–16 10.1007/BF01831719 MR0107973 0100.14002 CrossrefISIGoogle Scholar[11] R. Fletcher and , M. J. D. Powell, A rapidly convergent descent method for minimization, Comput. J., 6 (1963/1964), 163–168 MR0152116 0132.11603 CrossrefISIGoogle Scholar[12] M. J. Box, A comparison of several current optimization methods, and the use of transformations in constrained problems, Comput. J., 9 (1966), 67–77 MR0192645 0146.13304 CrossrefISIGoogle Scholar[13] Donald M. Topkis and , Arthur F. Veinott, on the convergence of some feasible direction algorithms for nonlinear programming, J. SIAM control, 5 (1967), 268–274 10.1137/0305018 0158.18805 LinkGoogle Scholar[14] Philip Wolfe, on the convergence of gradient methods under constraints, Rep., RZ-204, IBM watson research center, yorktown heights, new york, 1966 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Two efficient modifications of AZPRP conjugate gradient method with sufficient descent propertyJournal of Inequalities and Applications, Vol. 2022, No. 1 | 10 January 2022 Cross Ref Optimal Transport Based Seismic Inversion:Beyond Cycle SkippingCommunications on Pure and Applied Mathematics, Vol. 75, No. 10 | 1 April 2021 Cross Ref A robust BFGS algorithm for unconstrained nonlinear optimization problemsOptimization, Vol. 17 | 19 September 2022 Cross Ref Two Methods for the Implicit Integration of Stiff Reaction SystemsComputational Methods in Applied Mathematics, Vol. 0, No. 0 | 14 September 2022 Cross Ref Simple and fast convergent procedure to estimate recursive path analysis modelBehaviormetrika, Vol. 107 | 6 September 2022 Cross Ref Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functionsNumerical Algorithms, Vol. 91, No. 1 | 20 January 2022 Cross Ref A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization ProblemsMathematics, Vol. 10, No. 17 | 23 August 2022 Cross Ref Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamicsBIT Numerical Mathematics, Vol. 48 | 11 August 2022 Cross Ref An outlier-resistant κ -generalized approach for robust physical parameter estimationPhysica A: Statistical Mechanics and its Applications, Vol. 600 | 1 Aug 2022 Cross Ref An Active Set Trust-Region Method for Bound-Constrained OptimizationBulletin of the Iranian Mathematical Society, Vol. 48, No. 4 | 27 July 2021 Cross Ref Advancing Three-Dimensional Coupled Water Quality Model of Marine Ranches: Model Development, Global Sensitivity Analysis, and Optimization Based on Observation SystemJournal of Marine Science and Engineering, Vol. 10, No. 8 | 27 July 2022 Cross Ref Robust regression against heavy heterogeneous contaminationMetrika, Vol. 16 | 1 July 2022 Cross Ref A new class of nonlinear conjugate gradient coefficients for unconstrained optimizationAsian-European Journal of Mathematics, Vol. 15, No. 07 | 14 October 2021 Cross Ref New iterative conjugate gradient method for nonlinear unconstrained optimizationRAIRO - Operations Research, Vol. 56, No. 4 | 29 July 2022 Cross Ref Optimizing Oblique Projections for Nonlinear Systems using TrajectoriesSamuel E. Otto, Alberto Padovan, and Clarence W. RowleySIAM Journal on Scientific Computing, Vol. 44, No. 3 | 24 June 2022AbstractPDF (2764 KB)Variational methods for finding periodic orbits in the incompressible Navier–Stokes equationsJournal of Fluid Mechanics, Vol. 941 | 26 April 2022 Cross Ref LMBOPT: a limited memory method for bound-constrained optimizationMathematical Programming Computation, Vol. 14, No. 2 | 10 January 2022 Cross Ref Accelerated memory-less SR1 method with generalized secant equation for unconstrained optimizationCalcolo, Vol. 59, No. 2 | 11 March 2022 Cross Ref DiffPoseNet: Direct Differentiable Camera Pose Estimation2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) | 1 Jun 2022 Cross Ref A modified secant equation quasi-Newton method for unconstrained optimizationJournal of Applied Mathematics and Computing, Vol. 30 | 31 May 2022 Cross Ref Coupled support tensor machine classification for multimodal neuroimaging dataStatistical Analysis and Data Mining: The ASA Data Science Journal, Vol. 10 | 23 May 2022 Cross Ref A new hybrid conjugate gradient method of unconstrained optimization methodsAsian-European Journal of Mathematics, Vol. 15, No. 04 | 18 June 2021 Cross Ref A link between the steepest descent method and fixed-point iterationsOptimization Letters, Vol. 69 | 18 March 2022 Cross Ref A hybrid-line-and-curve search globalization technique for inexact Newton methodsApplied Numerical Mathematics, Vol. 173 | 1 Mar 2022 Cross Ref Development and Evaluation of Geometry Optimization Algorithms in Conjunction with ANI PotentialsJournal of Chemical Theory and Computation, Vol. 18, No. 2 | 12 January 2022 Cross Ref Nonlinear System Identification: Learning While Respecting Physical Models Using a Sequential Monte Carlo MethodIEEE Control Systems, Vol. 42, No. 1 | 1 Feb 2022 Cross Ref Visual analytics for nonlinear programming in robot motion planningJournal of Visualization, Vol. 25, No. 1 | 13 September 2021 Cross Ref Elastic wave full-waveform inversion in the time domain by the trust region methodJournal of Applied Geophysics, Vol. 197 | 1 Feb 2022 Cross Ref Adjoint Waveform Tomography of South AmericaJournal of Geophysical Research: Solid Earth, Vol. 127, No. 2 | 27 January 2022 Cross Ref A conjugate gradient algorithm based on double parameter scaled Broyden–Fletcher–Goldfarb–Shanno update for optimization problems and image restorationNeural Computing and Applications, Vol. 34, No. 1 | 13 August 2021 Cross Ref In-line viscosity identification via thermal-rheological measurements in an annular duct for polymer processingInternational Journal of Heat and Mass Transfer, Vol. 182 | 1 Jan 2022 Cross Ref Regularized elastic full-waveform inversion using deep learningAdvances in Subsurface Data Analytics | 1 Jan 2022 Cross Ref Nonlinear Optimization: A Brief OverviewNumerical Infinities and Infinitesimals in Optimization | 6 July 2022 Cross Ref Leveraging Joint-Diagonalization in Transform-Learning NMFIEEE Transactions on Signal Processing, Vol. 70 | 1 Jan 2022 Cross Ref Backtracking Gradient Descent Method and Some Applications in Large Scale Optimisation. Part 2: Algorithms and ExperimentsApplied Mathematics & Optimization, Vol. 84, No. 3 | 6 September 2020 Cross Ref Optical diffraction tomography from single-molecule localization microscopyOptics Communications, Vol. 499 | 1 Nov 2021 Cross Ref Constrained neural network training and its application to hyperelastic material modelingComputational Mechanics, Vol. 68, No. 5 | 3 August 2021 Cross Ref The Human Lumbar Spine During High-Rate Under Seat Loading: A Combined Metric Injury CriteriaAnnals of Biomedical Engineering, Vol. 49, No. 11 | 23 July 2021 Cross Ref Rayleigh Wave Dispersion Spectrum Inversion Across ScalesSurveys in Geophysics, Vol. 42, No. 6 | 19 October 2021 Cross Ref Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversionGeophysical Journal International, Vol. 228, No. 2 | 21 September 2021 Cross Ref Neural network method for solving parabolic two-temperature microscale heat conduction in double-layered thin films exposed to ultrashort-pulsed lasersInternational Journal of Heat and Mass Transfer, Vol. 178 | 1 Oct 2021 Cross Ref New hyrid conjugate gradient method as a convex combination of HZ and CD methodsAsian-European Journal of Mathematics, Vol. 14, No. 10 | 6 March 2021 Cross Ref Parallel Dislocation Model Implementation for Earthquake Source Parameter Estimation on Multi-Threaded GPUApplied Sciences, Vol. 11, No. 20 | 11 October 2021 Cross Ref Extended full waveform inversion with matching filterGeophysical Prospecting, Vol. 69, No. 7 | 24 June 2021 Cross Ref Full-waveform Inversion Based on q-Laplace DistributionPure and Applied Geophysics, Vol. 178, No. 9 | 24 August 2021 Cross Ref Modifications of Hestenes and Stiefel CG Method for Solving Unconstrained Optimization Problems2021 7th International Conference on Contemporary Information Technology and Mathematics (ICCITM) | 25 Aug 2021 Cross Ref A note on memory-less SR1 and memory-less BFGS methods for large-scale unconstrained optimizationNumerical Algorithms, Vol. 11 | 17 August 2021 Cross Ref A Descent Four-Term Conjugate Gradient Method with Global Convergence Properties for Large-Scale Unconstrained Optimisation ProblemsMathematical Problems in Engineering, Vol. 2021 | 14 Aug 2021 Cross Ref A modified conjugate gradient-based Elman neural networkCognitive Systems Research, Vol. 68 | 1 Aug 2021 Cross Ref On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risksStatistica Neerlandica, Vol. 75, No. 3 | 2 March 2021 Cross Ref A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization ProblemsAlgorithms, Vol. 14, No. 8 | 28 July 2021 Cross Ref Robust parameter estimation based on the generalized log-likelihood in the context of Sharma-Taneja-Mittal measurePhysical Review E, Vol. 104, No. 2 | 6 August 2021 Cross Ref Geodesic density regression for correcting 4DCT pulmonary respiratory motion artifactsMedical Image Analysis, Vol. 72 | 1 Aug 2021 Cross Ref Optimisation of Parameters in a German Bight Circulation Model by 4DVAR Assimilation of Current and Water Level ObservationsFrontiers in Marine Science, Vol. 8 | 29 July 2021 Cross Ref ASLR: An Adaptive Scheduler for Learning Rate2021 International Joint Conference on Neural Networks (IJCNN) | 18 Jul 2021 Cross Ref A Convex Combination between Two Different Search Directions of Conjugate Gradient Method and Application in Image RestorationMathematical Problems in Engineering, Vol. 2021 | 13 Jul 2021 Cross Ref An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy ConditionJournal of the Operations Research Society of China, Vol. 9, No. 2 | 12 July 2019 Cross Ref Direct Energy Minimization Based on Exponential Transformation in Density Functional Calculations of Finite and Extended SystemsComputer Physics Communications | 1 Jun 2021 Cross Ref A new three-term spectral conjugate gradient algorithm with higher numerical performance for solving large scale optimization problems based on Quasi-Newton equationInternational Journal of Modeling, Simulation, and Scientific Computing | 31 May 2021 Cross Ref Robust approaches for inverse problems based on Tsallis and Kaniadakis generalised statisticsThe European Physical Journal Plus, Vol. 136, No. 5 | 11 May 2021 Cross Ref Stochastic quasi-Newton with line-search regularisationAutomatica, Vol. 127 | 1 May 2021 Cross Ref An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization ProblemJournal of Mathematics, Vol. 2021 | 26 Apr 2021 Cross Ref A new hybrid conjugate gradient algorithm as a convex combination of MMWU and RMIL nonlinear problemsJournal of Interdisciplinary Mathematics, Vol. 24, No. 3 | 18 March 2021 Cross Ref Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithmsJournal of Choice Modelling, Vol. 38 | 1 Mar 2021 Cross Ref A Modified Descent Spectral Conjugate Gradient Method for Unconstrained OptimizationIranian Journal of Science and Technology, Transactions A: Science, Vol. 45, No. 1 | 31 October 2020 Cross Ref QSSR Modeling of Bacillus Subtilis Lipase A Peptide Collision Cross-Sections in Ion Mobility Spectrometry: Local Descriptor Versus Global DescriptorThe Protein Journal, Vol. 40, No. 1 | 16 January 2021 Cross Ref Numerical optimization of a multiphysics calculation scheme based on partial convergenceAnnals of Nuclear Energy, Vol. 151 | 1 Feb 2021 Cross Ref A new accelerated diagonal quasi-Newton updating method with scaled forward finite differences directional derivative for unconstrained optimizationOptimization, Vol. 70, No. 2 | 16 January 2020 Cross Ref A Three-Term Gradient Descent Method with Subspace TechniquesMathematical Problems in Engineering, Vol. 2021 | 7 Jan 2021 Cross Ref Implementing and modifying Broyden class updates for large scale optimizationComputational Optimization and Applications, Vol. 78, No. 1 | 9 November 2020 Cross Ref Set-point optimization in wind farms to mitigate effects of flow blockage induced by atmospheric gravity wavesWind Energy Science, Vol. 6, No. 1 | 5 February 2021 Cross Ref Statistics and Numerical MethodsPattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors | 23 November 2020 Cross Ref A training algorithm with selectable search direction for complex-valued feedforward neural networksNeural Networks, Vol. 40 | 1 Jan 2021 Cross Ref A decent three term conjugate gradient method with global convergence properties for large scale unconstrained optimization problemsAIMS Mathematics, Vol. 6, No. 10 | 1 Jan 2021 Cross Ref Adaptive Learning Rate and Momentum for Training Deep Neural NetworksMachine Learning and Knowledge Discovery in Databases. Research Track | 11 September 2021 Cross Ref A Quasi‐Newton Reformulated Geostatistical Approach on Reduced Dimensions for Large‐Dimensional Inverse ProblemsWater Resources Research, Vol. 57, No. 1 | 22 January 2021 Cross Ref Manifold Optimization for High-Accuracy Spatial Location Estimation Using Ultrasound WavesIEEE Transactions on Signal Processing, Vol. 69 | 1 Jan 2021 Cross Ref Basic Descent MethodsLinear and Nonlinear Programming | 20 August 2021 Cross Ref Taking the 4D Nature of fMRI Data Into Account Promises Significant Gains in Data CompletionIEEE Access, Vol. 9 | 1 Jan 2021 Cross Ref Approaching the full configuration interaction ground state from an arbitrary wavefunction with gradient descent and quasi-Newton algorithmsThe Journal of Chemical Physics, Vol. 153, No. 23 | 21 Dec 2020 Cross Ref Customized Federated Learning for accelerated edge computing with heterogeneous task targetsComputer Networks, Vol. 183 | 1 Dec 2020 Cross Ref Hybrid Riemannian conjugate gradient methods with global convergence propertiesComputational Optimization and Applications, Vol. 77, No. 3 | 5 September 2020 Cross Ref A one-parameter class of three-term conjugate gradient methods with an adaptive parameter choiceOptimization Methods and Software, Vol. 35, No. 6 | 13 September 2018 Cross Ref Gaussian Process Regression for Maximum Entropy DistributionJournal of Computational Physics, Vol. 418 | 1 Oct 2020 Cross Ref A new non-linear conjugate gradient algorithm for destructive cure rate model and a simulation study: illustration with negative binomial competing risksCommunications in Statistics - Simulation and Computation, Vol. 6 | 10 September 2020 Cross Ref A double parameter self-scaling memoryless BFGS method for unconstrained optimizationComputational and Applied Mathematics, Vol. 39, No. 3 | 2 June 2020 Cross Ref Adaptive type-2 neural fuzzy sliding mode control of a class of nonlinear systemsNonlinear Dynamics, Vol. 101, No. 4 | 18 August 2020 Cross Ref A modified nonlinear Polak–Ribière–Polyak conjugate gradient method with sufficient descent propertyCalcolo, Vol. 57, No. 3 | 26 August 2020 Cross Ref Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance caseMathematical Methods of Operations Research, Vol. 92, No. 1 | 12 February 2020 Cross Ref Probing depth and lateral variations of upper-mantle seismic anisotropy from full-waveform inversion of teleseismic body-wavesGeophysical Journal International, Vol. 222, No. 1 | 20 April 2020 Cross Ref High-resolution reservoir characterization using deep learning-aided elastic full-waveform inversion: The North Sea field data exampleGEOPHYSICS, Vol. 85, No. 4 | 8 May 2020 Cross Ref Estimation of Beta-Pareto Distribution Based on Several Optimization MethodsMathematics, Vol. 8, No. 7 | 1 July 2020 Cross Ref Multi‐parameter reflection waveform inversion for acoustic transversely isotropic media with a vertical symmetry axisGeophysical Prospecting, Vol. 68, No. 6 | 17 June 2020 Cross Ref The application of nonlinear least-squares estimation algorithms in atmospheric density model calibrationAircraft Engineering and Aerospace Technology, Vol. 92, No. 7 | 20 May 2020 Cross Ref Decreasing the uncertainty of analysis using numerical algorithms robust to and of Scientific Vol. 91, No. 6 | 1 Jun 2020 Cross Ref An Efficient Three-Term Method for Models in Regression Vol. 8, No. 6 | 15 June 2020 Cross Ref of the by Finite for Unconstrained of Optimization Theory and Applications, Vol. No. 3 | 10 May 2020 Cross Ref New conjugate gradient algorithms based on self-scaling memoryless Broyden–Fletcher–Goldfarb–Shanno Vol. 57, No. 2 | 18 May 2020 Cross Ref A class of convergent three-term conjugate gradient methodsApplied Numerical Mathematics, Vol. 151 | 1 May 2020 Cross Ref A neural Conjugate gradient algorithm and its convergence Sciences, Vol. | 1 May 2020 Cross Ref Three-Dimensional Regularized A from the Vol. 10, No. 5 | 22 May 2020 Cross Ref On Quasi‐Newton methods in fast Journal for Numerical Methods in Engineering, Vol. No. 8 | 23 2019 Cross Ref Some three-term conjugate gradient methods with the new direction Numerical Mathematics, Vol. | 1 Apr 2020 Cross Ref Analysis of the gradient method with an search on a class of convex Methods and Software, Vol. 35, No. 2 | 9 October 2019 Cross Ref search methods for global of Mathematics and Vol. No. | 27 August 2019 Cross Ref Adaptive Control of a Using a Neural Journal for Science and Engineering, Vol. 45, No. 3 | 21 January 2020 Cross Ref A on Optimization Algorithms in of Conference Vol. No. 1 | 1 Mar 2020 Cross Ref Global Convergence of the to a Computation, Vol. No. 1 | 1 Mar 2020 Cross Ref Using a Conjugate Gradient Regression Resources Research, Vol. No. 1 | 27 June 2019 Cross Ref optimization in using gradient descent Vol. | 1 Feb 2020 Cross Ref for from diffraction Vol. No. 1 | 1 January 2020 Cross Ref using and neural Visual Vol. No. 1 | 22 August 2018 Cross Ref A New Hybrid Method for Unconstrained Differentiable of Nonlinear | 20 February 2020 Cross Ref Quasi-Newton Optimization Methods for Deep Learning Learning Applications | 29 February 2020 Cross Ref by edge with Gaussian of Vol. No. 1 | 9 August 2019 Cross Ref of Mathematical Optimization Problems | 1 October 2020 Cross Ref An efficient solution scheme for in a Methods in Applied Mechanics and Engineering, Vol. | 1 Jan 2020 Cross Ref Image and Estimation with International on Computational in Adaptive | 1 Dec 2019 Cross Ref A new accelerated conjugate gradient method for large-scale unconstrained optimizationJournal of Inequalities and Applications, Vol. No. 1 | 20 November 2019 Cross Ref Research of estimation methods for full waveform inversion in time Geophysics, Vol. No. 6 | 17 September 2019 Cross Ref elastic full-waveform Vol. 84, No. 6 | 16 October 2019 Cross Ref A Hybrid of Quasi-Newton Method with CG Method for Unconstrained of Conference Vol. No. 1 | 1 Nov 2019 Cross Ref Conjugate gradient-based fuzzy neural network parameter identification and its convergence Vol. | 1 Oct 2019 Cross Ref Regularized elastic full-waveform inversion using deep Vol. 84, No. 5 | 24 August 2019 Cross Ref and Parallel Learning Algorithms Learning Rate in and Vol. 6 | 27 August 2019 Cross Ref of Networks via CompletionIEEE Transactions on Communications, Vol. No. 8 | 1 Aug 2019 Cross Ref A diagonal quasi-Newton updating method for unconstrained optimizationNumerical Algorithms, Vol. No. 2 | 29 June 2018 Cross Ref A New Quasi-Newton Method Finite for Unconstrained Functional Analysis and Optimization, Vol. 6 | 20 May 2019 Cross Ref Efficient by of Chemical Theory and Computation, Vol. 15, No. 5 | 2 April 2019 Cross Ref An efficient adaptive three-term of the conjugate gradient Methods and Software, Vol. 34, No. 3 | 15 October 2018 Cross Ref A Quasi-Newton Algorithm on the Manifold for with 2019 - 2019 International Conference on and Signal | 1 May 2019 Cross Ref of the and from Mathematical Modelling, Vol. 68 | 1 Apr 2019 Cross Ref inversion of data using an application for the estimation of the Journal International, Vol. No. 1 | 17 January 2019 Cross Ref An Estimation Algorithm for Models with Spatial of the Society of Vol. No. 2 | 5 March 2019 Cross Ref The of and A Journal of the Vol. 8, No. 1 | 22 March 2018 Cross Ref The Optimal Location of Vol. 9, No. 3 | 27 February 2019 Cross Ref Convergence Rate of Descent Method with New on Riemannian of Optimization Theory and Applications, Vol. No. 3 | 24 September 2018 Cross Ref in Hybrid and Transactions on Signal and Information Networks, Vol. No. 1 | 1 Mar 2019 Cross Ref A new hybrid approach for optimization of Vol. No. 2 | 24 April 2019 Cross Ref for Hybrid Transactions on Vol. 49, No. 2 | 1 Feb 2019 Cross Ref A New Conjugate Gradient Method with Optimal Parameter Functional Analysis and Optimization, Vol. 40, No. 2 | 20 November 2018 Cross Ref of Models of Networks | 14 2018 Cross Ref the distribution of to on using Vol. | 1 Jan 2019 Cross Ref A Quasi-Newton Algorithm for Optimizing with G. and Journal on Optimization, Vol. No. 2 | 11 April 2019 Cross Ref 2019 Cross Ref Unconstrained Optimization | 10 November 2019 Cross Ref Optimization and Simulation | 2 January 2020 Cross Ref New Hybrid Conjugate Gradient Method A Convex Combination of and Vol. 39, No. 1 | 4 January 2019 Cross Ref optimization via a and a Control, Optimisation and of Vol. 25 | 5 April 2019 Cross Ref in quasi-Newton Programming Computation, Vol. 10, No. 4 | 12 February 2018 Cross Ref An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy ConditionJournal of Optimization Theory and Applications, Vol. No. 3 | 28 August 2018 Cross Ref the properties of International Conference on and | 1 Dec 2018 Cross Ref A New Conjugate Gradient Algorithm for Training in Neural Transactions on Neural Networks and Learning Systems, Vol. No. 12 | 1 Dec 2018 Cross Ref waveform inversion in time and domain of in seismic a Research Journal, Vol. No. 4 | 1 October 2018 Cross Ref A diagonal quasi-Newton updating method based on the function of and for unconstrained optimizationOptimization, Vol. No. 9 | 17 June 2018 Cross Ref in parameter and time estimation for Vol. | 1 2018 Cross Ref Optimal control of systems using hybrid numerical optimization Vol. No. 8 | 2 May 2018 Cross Ref Analysis by Transactions on Signal Processing, Vol. No. 15 | 1 Aug 2018 Cross Ref of large-scale systems in of Applied Physics, Vol. No. 4 | 28 Jul 2018 Cross Ref A Method for Nonlinear Problems Based on for Systems - Modeling, and | 18 July 2018 Cross Ref A hybrid conjugate gradient image approach for Science Journal, Vol. No. 5 | 16 February 2018 Cross Ref A Coupled with an Gradient Method and Application to ProblemsMathematical Problems in Engineering, Vol. 2018 | 2 Jul 2018 Cross Ref Optimization approach for the Vol. No. 4 | 1 Jul 2018 Cross Ref A Broyden–Fletcher–Goldfarb–Shanno Method Based on Minimizing the Function of and for Unconstrained of Optimization Theory and Applications, Vol. 178, No. 1 | 4 May 2018 Cross Ref by a modified Newton method using Physics and Vol. No. 6 | 18 April 2018 Cross Ref A on the via and Analysis, Vol. No. 2 | 17 February 2018 Cross Ref Some three-term conjugate gradient methods with the inexact search Vol. No. 2 | 16 March 2018 Cross Ref of Science and Technology, Vol. No. 3 | 25 May 2018 Cross Ref of deep

We compare the network of aggregated journal-journal citation relations provided by the Journal Citation Reports (JCR) 2012 of the Science and Social Science Citation Indexes (SCI and SSCI) with similar data based on Scopus 2012. First, global maps were developed for the two sets separately; sets of documents can then be compared using overlays to both maps. Using fuzzy-string matching and ISSN numbers, we were able to match 10,524 journal names between the two sets; that is, 96.4% of the 10,936 journals contained in JCR or 51.2% of the 20,554 journals covered by Scopus. Network analysis was then pursued on the set of journals shared between the two databases and the two sets of unique journals. Citations among the shared journals are more comprehensively covered in JCR than Scopus, so the network in JCR is denser and more connected than in Scopus. The ranking of shared journals in terms of indegree (that is, numbers of citing journals) or total citations is similar in both databases overall (Spearman's \r{ho} > 0.97), but some individual journals rank very differently. Journals that are unique to Scopus seem to be less important--they are citing shared journals rather than bein

Rankings of scholarly journals based on citation data are often met with skepticism by the scientific community. Part of the skepticism is due to disparity between the common perception of journals' prestige and their ranking based on citation counts. A more serious concern is the inappropriate use of journal rankings to evaluate the scientific influence of authors. This paper focuses on analysis of the table of cross-citations among a selection of Statistics journals. Data are collected from the Web of Science database published by Thomson Reuters. Our results suggest that modelling the exchange of citations between journals is useful to highlight the most prestigious journals, but also that journal citation data are characterized by considerable heterogeneity, which needs to be properly summarized. Inferential conclusions require care in order to avoid potential over-interpretation of insignificant differences between journal ratings. Comparison with published ratings of institutions from the UK's Research Assessment Exercise shows strong correlation at aggregate level between assessed research quality and journal citation `export scores' within the discipline of Statistics.

In spite of the tremendous increase in the rate at which protein structures are being determined, there is still an enormous gap between the numbers of known DNA-derived sequences and the numbers of three-dimensional structures. In order to shed light on the biological functions of the molecules, researchers often resort to comparative molecular modeling. Earlier work has shown that when the sequence alignment is in error, then the comparative model is guaranteed to be wrong. In addition, loops, the sites of insertions and deletions in families of homologous proteins, are exceedingly difficult to model. Thus, many of the current problems in comparative molecular modeling are minor versions of the global protein folding problem. In order to assess objectively the current state of comparative molecular modeling, 13 groups submitted blind predictions of seven different proteins of undisclosed tertiary structure. This assessment shows that where sequence identity between the target and the template structure is high (> 70%), comparative molecular modeling is highly successful. On the other hand, automated modeling techniques and sophisticated energy minimization methods fail to improve upon the starting structures when the sequence identity is low (approximately 30%). Based on these results it appears that insertions and deletions are still major problems. Successfully deducing the correct sequence alignment when the local similarity is low is still difficult. We suggest some minimal testing of submitted coordinates that should be required of authors before papers on comparative molecular modeling are accepted for publication in journals.

A review of the mechanisms of speciation is performed. The mechanisms of the evolution of species, taking into account the feedback of the state of the environment and mechanisms of the emergence of complexity, are considered. It is shown that these mechanisms, at the molecular level, cannot work steadily in terms of classical mechanics. Quantum mechanisms of changes in the genome, based on the long-range interaction potential between biologically important molecules, are proposed as one of possible explanation. Different variants of interactions of the organism and environment based on molecular recognition and leading to new species origins are considered. Experiments to verify the model are proposed. This bio-physical study is completed by the general operational model of based on quantum information theory. The latter is applied to model epigenetic evolution.

This study examines the social media uptake of scientific journals on two different platforms - X and WeChat - by comparing the adoption of X among journals indexed in the Science Citation Index-Expanded (SCIE) with the adoption of WeChat among journals indexed in the Chinese Science Citation Database (CSCD). The findings reveal substantial differences in platform adoption and user engagement, shaped by local contexts. While only 22.7% of SCIE journals maintain an X account, 84.4% of CSCD journals have a WeChat official account. Journals in Life Sciences & Biomedicine lead in uptake on both platforms, whereas those in Technology and Physical Sciences show high WeChat uptake but comparatively lower presence on X. User engagement on both platforms is dominated by low-effort interactions rather than more conversational behaviors. Correlation analyses indicate weak-to-moderate relationships between bibliometric indicators and social media metrics, confirming that online engagement reflects a distinct dimension of journal impact, whether on an international or a local platform. These findings underscore the need for broader social media metric frameworks that incorporate locally dom

An exploratory, descriptive analysis is presented of the national orientation of scientific, scholarly journals as reflected in the affiliations of publishing or citing authors. It calculates for journals covered in Scopus an Index of National Orientation (INO), and analyses the distribution of INO values across disciplines and countries, and the correlation between INO values and journal impact factors. The study did not find solid evidence that journal impact factors are good measures of journal internationality in terms of the geographical distribution of publishing or citing authors, as the relationship between a journal's national orientation and its citation impact is found to be inverse U-shaped. In addition, journals publishing in English are not necessarily internationally oriented in terms of the affiliations of publishing or citing authors; in social sciences and humanities also USA has their nationally oriented literatures. The paper examines the extent to which nationally oriented journals entering Scopus in earlier years, have become in recent years more international. It is found that in the study set about 40 per cent of such journals does reveal traces of internati

Overlay journals are characterised by their articles being published on open access repositories, often already starting in their initial preprint form as a prerequisite for submission to the journal prior to initiating the peer-review process. In this study we aimed to identify currently active overlay journals and examine their characteristics. We utilised an explorative web search and contacted key service providers for additional information. The final sample consisted of 34 overlay journals. While the results show that new overlay journals have been actively established within recent years, the current presence of overlay journals remains diminutive compared to the overall number of open access journals. Most overlay journals publish articles in natural sciences, mathematics or computer sciences, and are commonly published by groups of academics rather than formal organisations. They may also rank highly within the traditional journal citation metrics. None of the investigated journals required fees from authors, which is likely related to the cost-effective aspects of the overlay publishing model. Both the growth in adoption of open access preprint repositories and researcher

Using the Scopus dataset (1996-2007) a grand matrix of aggregated journal-journal citations was constructed. This matrix can be compared in terms of the network structures with the matrix contained in the Journal Citation Reports (JCR) of the Institute of Scientific Information (ISI). Since the Scopus database contains a larger number of journals and covers also the humanities, one would expect richer maps. However, the matrix is in this case sparser than in the case of the ISI data. This is due to (i) the larger number of journals covered by Scopus and (ii) the historical record of citations older than ten years contained in the ISI database. When the data is highly structured, as in the case of large journals, the maps are comparable, although one may have to vary a threshold (because of the differences in densities). In the case of interdisciplinary journals and journals in the social sciences and humanities, the new database does not add a lot to what is possible with the ISI databases.

The understanding of molecular cell biology requires insight into the structure and dynamics of networks that are made up of thousands of interacting molecules of DNA, RNA, proteins, metabolites, and other components. One of the central goals of systems biology is the unraveling of the as yet poorly characterized complex web of interactions among these components. This work is made harder by the fact that new species and interactions are continuously discovered in experimental work, necessitating the development of adaptive and fast algorithms for network construction and updating. Thus, the "reverse-engineering" of networks from data has emerged as one of the central concern of systems biology research. A variety of reverse-engineering methods have been developed, based on tools from statistics, machine learning, and other mathematical domains. In order to effectively use these methods, it is essential to develop an understanding of the fundamental characteristics of these algorithms. With that in mind, this chapter is dedicated to the reverse-engineering of biological systems. Specifically, we focus our attention on a particular class of methods for reverse-engineering, namely th

Abstract Experiments were conducted to determine the solubilities of H2O and CO2 and the nature of their mixing behavior in basaltic liquid at pressures and temperature relevant to seqfloor eruption. Mid-ocean ridge basaltic (MORB) liquid was equilibrated at 1200°C with pure H2O at pressures of 176–717 bar and H2O—CO2 vapor at pressures up to 980 bar. Concentrations and speciation of H2O and CO2 dissolved in the quenched glasses were measured using IR spectroscopy. Molar absorptivities for the 4500 cm−1 band of hydroxyl groups and the 5200 and 1630 cm−1 bands of molecular water are 0⋅67±0⋅03, 0⋅62±0⋅07, and 25±3 l/mol-cm, respectively. These and previously determined molar absorptivities for a range of silicate melt compositions correlate positively and linearly with the concentration of tetrahedral cations (Si+Al). The speciation of water in glass quenched from vapor-saturated basaltic melt is similar to that determined by Silver & Stolper (Journal of Petrology30, 667–709, 1989) in albitic glass and can be fitted by their regular ternary solution model using the coefficients for albitic glasses. Concentrations of molecular water measured in the quenched basaltic glasses are proportional to f H2O in all samples regardless of the composition of the vapor, demonstrating that the activity of molecular water in basaltic melts follows Henry's law at these pressures. A best fit to our data and existing higher-pressure water solubility data (Khitarov et al., Geochemistry5, 479–492, 1959; Hamilton et al., Journal of Petrology5, 21–39, 1964), assuming Henrian behavior for molecular water and that the dependence of molecular water content on total water content can be described by the regular solution model, gives estimates for the Vo, mH2O of 12±1 cm3/mol and for the 1-bar water solubility of 0⋅11 wt%. Concentrations of CO2 dissolved as carbonate in the melt for pure CO2-saturated and mixed H2O-CO2-saturated experiments are a simple function of fCO2 These results suggest Henrian behavior for the activity of carbonate in basaltic melt and do not support the widely held view that water significantly enhances the solution of carbon dioxide in basaltic melts. Using a ΔVo, mr of 23 cm3/mol (Pan et al., Geochimica et Cosmochimica Acta55, 1587–1595, 1991), the solubility of carbonate in the melt at 1 bar and 1200°C is 0⋅5 p.p.m. Our revised determination of CO2 solubility is ∼20% higher than that reported by Stolper & Holloway (Earth and Planetary Science Letters87, 397–408, 1988).

Using three years of the Journal Citation Reports (2011, 2012, and 2013), indicators of transitions in 2012 (between 2011 and 2013) are studied using methodologies based on entropy statistics. Changes can be indicated at the level of journals using the margin totals of entropy production along the row or column vectors, but also at the level of links among journals by importing the transition matrices into network analysis and visualization programs (and using community-finding algorithms). Seventy-four journals are flagged in terms of discontinuous changes in their citations; but 3,114 journals are involved in "hot" links. Most of these links are embedded in a main component; 78 clusters (containing 172 journals) are flagged as potential "hot spots" emerging at the network level. An additional finding is that PLoS ONE introduced a new communication dynamics into the database. The limitations of the methodology are elaborated using an example. The results of the study indicate where developments in the citation dynamics can be considered as significantly unexpected. This can be used as heuristic information; but what a "hot spot" in terms of the entropy statistics of aggregated cit

Defining and measuring internationality as a function of influence diffusion of scientific journals is an open problem. There exists no metric to rank journals based on the extent or scale of internationality. Measuring internationality is qualitative, vague, open to interpretation and is limited by vested interests. With the tremendous increase in the number of journals in various fields and the unflinching desire of academics across the globe to publish in "international" journals, it has become an absolute necessity to evaluate, rank and categorize journals based on internationality. Authors, in the current work have defined internationality as a measure of influence that transcends across geographic boundaries. There are concerns raised by the authors about unethical practices reflected in the process of journal publication whereby scholarly influence of a select few are artificially boosted, primarily by resorting to editorial maneuvres. To counter the impact of such tactics, authors have come up with a new method that defines and measures internationality by eliminating such local effects when computing the influence of journals. A new metric, Non-Local Influence Quotient(NLI