Previous article Next article Some Applications of the Pseudoinverse of a MatrixT. N. E. GrevilleT. N. E. Grevillehttps://doi.org/10.1137/1002004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] T. N. E. Greville, The pseudoinverse of a rectangular or singular matrix and its application to the solution of systems of linear equations, SIAM Rev., 1 (1959), 38–43 10.1137/1001003 MR0101615 0123.11202 LinkISIGoogle Scholar[2] E. H. Moore, , Bull. Amer. Math. Soc., 26 (1920), 394–395 Google Scholar[3] E. H. Moore, General Analysis, Mem. Amer. Philos. Soc., 1 (1935), 197–209, Part 1 0013.11605 Google Scholar[4] Arne Bjerhammar, Application of calculus of matrices to method of least squares with special reference to geodetic calculations, Trans. Roy. Inst. Tech. Stockholm, 1951 (1951), 86 pp. (2 plates) MR0055793 0043.12203 Google Scholar[5] Arne Bjerhammar, Rectangular reciprocal matrices, with special reference to geodetic calculations, Bull. Géodésique, 1951 (1951), 188–220 MR0043758 CrossrefGoogle Scholar[6] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[7] T. N. E. Greville, The pseudoinverse of a rectangular matrix and its statistical applications, Amer. Statist. Assoc., Proc. Soc. Statist. Sect., 1958, 116–121, The numerical example is given only in the mimeographed version, available from the author Google Scholar[8] Benjamin A. Dent and , Albert Newhouse, Polynomials orthogonal over discrete domains, SIAM Rev., 1 (1959), 55–59 10.1137/1001008 MR0100340 0123.33003 LinkGoogle Scholar[9] George E. Forsythe, Generation and use of orthogonal polynomials for data-fitting with a digital computer, J. Soc. Indust. Appl. Math., 5 (1957), 74–88 10.1137/0105007 MR0092208 0083.35503 LinkISIGoogle Scholar[10] J. E. Barker, Use of orthogonal polynomials in fitting curves and estimating their first and second derivatives, NPG Report, 1553, U. S. Naval Proving Ground, Dahlgren, Va., 1958, NAVORD Report No. 5138, First Revision, June Google Scholar[11] R. A. Frazer, , W. J. Duncan and , A. R. Collar, Elementary Matrices, Cambridge, 1938 0021.22803 CrossrefGoogle Scholar[12] R. Penrose, On best approximation solutions of linear matrix equations, Proc. Cambridge Philos. Soc., 52 (1956), 17–19 MR0074092 0070.12501 CrossrefGoogle Scholar[13] T. N. E. Greville, On smoothing a finite table: A matrix approach, J. Soc. Indust. Appl. Math., 5 (1957), 137–154 10.1137/0105010 MR0092206 0080.36102 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Invited Tutorial: Analog Matrix Computing With Crosspoint Resistive Memory ArraysIEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 69, No. 7 | 1 Jul 2022 Cross Ref Blockwise Recursive Moore–Penrose Inverse for Network LearningIEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 52, No. 5 | 1 May 2022 Cross Ref The design of on-chip digital Fourier transform spectrometerSeventh Asia Pacific Conference on Optics Manufacture (APCOM 2021) | 15 Feb 2022 Cross Ref A pseudo-inverse decomposition-based self-organizing modular echo state network for time series predictionApplied Soft Computing, Vol. 116 | 1 Feb 2022 Cross Ref Online Newton Step Based on Pseudo-Inverse and Elementwise MultiplicationProceedings of 7th International Conference on Harmony Search, Soft Computing and Applications | 2 September 2022 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algorithm in results Transactions on Circuits and Systems, Vol. No. 10 | 1 Oct Cross Ref AND AND Vol. No. | 26 August Cross Ref A method with for linear Vol. No. 5 | 1 Jan Cross Ref numerical computation using Computing, Vol. 16, No. 1 | 1 Nov Cross Ref On the of with linear Transactions on Information Theory, Vol. 35, No. 4 | 1 Jul Cross Ref Linear and in neural Transactions on Information Theory, Vol. 35, No. 3 | 1 May Cross Ref and Memory | 1 Jan Cross Ref classification using a linear Vol. No. 6 | 1 Jan Cross Ref An algorithm for and in Vol. 5, No. 2 | 1 Jul Cross Ref of and learning on Networks | 1 June Cross Ref and Memory | 1 Jan Cross Ref An iterative for the generalized matrix Processing Vol. 26, No. 5 | 1 Jan Cross Ref inverses of Algebra and its Applications, Vol. | 1 Jun Cross Ref and using a linear Optics, Vol. 26, No. 10 | 15 May Cross Ref Learning and Theory and Applications | 1 Jan Cross Ref Neural Network for Efficient Information Systems and | 1 Jan Cross Ref for Redundant in International Journal of Research, Vol. No. 3 | 2 July 2016 Cross Ref An of the Matrix Journal on Vol. No. 3 | 2 August for the of Computer Vol. No. 3 | 1 Jul Cross Ref of Artificial and Computer of their and of Robots and | 1 Jan Cross Ref for Vol. No. 4 | 1 Jan Cross Ref A analysis for the and Vol. 31, No. 3 | 1 Sep Cross Ref Optimal with Vol. No. 2 | 1 Jul Cross Ref analysis Journal of Vol. No. 1 | 1 Jan Cross Ref A SINGULAR Vol. No. | 19 July 2013 Cross Ref Computation of inverse of a special of Mathematics with Applications, Vol. No. 4 | 1 Jan Cross Ref Optimal Control by An Vol. No. 5 | 1 Jan Cross Ref via and Control Conference | August 2012 Cross Ref Theory and of matrix with to matrices and Journal of Systems Science, Vol. No. 4 | 1 Apr Cross Ref for the solution of linear Analysis Methods in Analysis | 24 August Cross Ref computing for the generalized inverse and the of their Vol. 2, No. 1 | 1 Jan Cross Ref OF A under the Mathematical Task by the Naval Systems Applied Mathematics and | 1 Jan Cross Ref Pseudoinverse and recursive of in Mathematical Journal, Vol. No. 1 | 1 Jan Cross Ref Analysis of with Hessian from Vol. No. 5 | 1 Jan Cross Ref On for least squares solutions and of Computational and Applied Mathematics, Vol. No. 4 | 1 Dec Cross Ref A Weighted Inverse Algorithm for Transactions on Vol. No. 10 | 1 Oct Cross Ref An iterative procedure for nonlinear of Mathematical Analysis and Applications, Vol. No. 3 | 1 May Cross Ref to of Computational Mathematics and Mathematical Vol. No. 5 | 1 Jan Cross Ref on of Journal, Vol. 14, No. 11 | 1 Nov Cross Ref on of the Inverse of a Journal, Vol. 14, No. 11 | 1 Nov Cross Ref by to E. Journal, Vol. 14, No. 11 | 1 Nov Cross Ref Singular Decomposition and the Moore–Penrose Inverse of E. Journal on Applied Mathematics, Vol. 31, No. 1 | 12 July of to and and Applications | 1 Jan Cross Ref on and and Applications | 1 Jan Cross Ref A generalized pseudoinverse algorithm for Journal of Systems Science, Vol. No. 12 | 1 Dec Cross Ref inverses of Algebra and its Applications, Vol. No. 2 | 1 Apr Cross Ref GENERALIZED AND Sciences, Vol. No. 2 | 1 Apr Cross Ref Computational of matrix generalized inversion for the with Mathematics with Applications, Vol. No. 1 | 1 Jan Cross Ref for of Statistical Computation and Vol. No. 3 | 1 Jan Cross Ref Analysis of the of MatricesJournal of the Statistical Vol. 69, No. | 1 Dec Cross Ref On the solution of the linear least squares and Vol. No. | 1 Sep Cross Ref The of an and the of in RegressionJournal of the Statistical Vol. 69, No. | 1 Mar Cross Ref inverses of Algebra and its Applications, Vol. No. 1 | 1 Feb Cross Ref Vol. No. | 6 September 2013 Cross Ref matrix Journal of Mathematics, Vol. No. 3 | 1 Sep Cross Ref The Pseudo-Inverse of a Journal on Applied Mathematics, Vol. No. 4 | Pseudoinverse of a Matrix of T. L. and T. A. Journal on Applied Mathematics, Vol. No. 4 | product of with Mathematical Journal, Vol. No. 3 | 1 Jan Cross Ref for the Moore-Penrose inverse of a of the of Statistical Mathematics, Vol. No. 1 | 1 Dec Cross Ref Linear classification Transactions on Information Theory, Vol. No. 5 | 1 Sep Cross Ref On in singular and a of pseudo-inverse of a Journal of Vol. No. 6 | 3 April Cross Ref is in by No. 2 of | 1 Jan Cross Ref and the Moore-Penrose Pseudoinverse | 1 Jan Cross Ref Inverse in Vol. No. | 1 Jan Cross Ref with singular Vol. No. 6 | 1 Dec Cross Ref Representations for and for Algebra and its Applications, Vol. No. 3 | 1 Jul Cross Ref A new method for reduction of Journal of Vol. 14, No. 1 | 1 Jul Cross Ref and Iteration for Singular Functional Analysis and Applications | 1 Jan Cross Ref Optimal using generalized General and of Computation, Vol. No. | 1 January Cross Ref of linear of Mathematical Analysis and Applications, Vol. 31, No. 3 | 1 Sep Cross Ref Linear and Nonlinear Vol. 12, No. 3 | 1 Aug Cross Ref A Pseudoinverse and Application to Constrained and Journal on Applied Mathematics, Vol. No. 1 | 12 July KB)An of the Moore–Penrose Inverse of an Vol. 12, No. 1 | 18 July feature in a of Transactions on Information Theory, Vol. 16, No. 1 | 1 Jan Cross Ref On the Computation of the Inverse of Matrices with Symbolic Analysis and Matrix Algebra Cross Ref A recursive algorithm and for and International Cross Ref of and by and International Conference on Cross Ref for of IEEE/RSJ International Conference on Intelligent Robots and Systems Cross Ref method for matrix of the projection algorithm using International on Circuits and Cross Ref Efficient method for the of the inverse International Conference on and Cross Ref in for International Conference on and Cross Ref application of Inverse TheoryJournal of Research, Vol. 74, No. 10 | September 2012 Cross Ref A Note on Matrices and Vol. 11, No. 2 | 18 July for and Nonnegative in of Journal on Applied Mathematics, Vol. No. 2 | 12 July of Vol. No. 1 | 1 Mar Cross Ref Inverse Vol. No. | 1 Jan Cross Ref A method for the of Computation, Vol. No. | 1 January Cross Ref A on generalized Vol. No. 4 | 29 October 2013 Cross Ref of of a E. Journal on Analysis, Vol. 5, No. 1 | July pseudoinverse solutions to linear of Optimization Theory and Applications, Vol. 2, No. 2 | 1 Mar Cross Ref A Method for Matrix Journal on Analysis, Vol. No. 4 | July Note on and the Journal on Analysis, Vol. No. 4 | July the of in Journal on Applied Mathematics, Vol. No. 5 | 13 July generalized inverses and on the of with application to iterative of Mathematical Analysis and Applications, Vol. No. 3 | 1 Jun Cross Ref On and of the Journal on Applied Mathematics, Vol. No. 2 | 13 July of Efficient Linear Transactions on and Systems, Vol. No. 2 | 1 Mar Cross Ref An method for computing the generalized of Computation, Vol. No. | 1 January Cross Ref A Method for Computing the Inverse of a Journal on Analysis, Vol. No. 4 | July the Order to the Inverse of Matrix of the Vol. No. 3 | 1 Jul Cross Ref and S. Journal on Applied Mathematics, Vol. 14, No. 2 | 13 July in Journal on Applied Mathematics, Vol. 14, No. 3 | 28 July Control of Linear Systems with in in of for the by the Applied of in Control Systems | 1 Jan Cross Ref Cross Ref Representations for the Inverse of of E. of the for and Applied Mathematics Analysis, Vol. 2, No. 1 | 3 August the Singular and Pseudo-Inverse of a and W. of the for and Applied Mathematics Analysis, Vol. 2, No. 2 | July Least Squares of Linear E. of the for and Applied Mathematics Analysis, Vol. 2, No. 2 | July Least Squares with of the Statistical Vol. No. | 1 Dec Cross Ref Representations for the Inverse of a E. of the for and Applied Mathematics, Vol. 12, No. 3 | 13 July of and in analysis for Vol. No. 3 | 1 Sep Cross Ref and Basic to Singular Linear of the for and Applied Mathematics, Vol. 12, No. 1 | 13 July on the Inverse of the Product of E. Vol. No. 1 | 18 July Computer Control and Application to in Control Systems | 1 Jan Cross Ref to the Theory of and A. of the for and Applied Mathematics, Vol. 11, No. 3 | 13 July Note on A. and H. of the for and Applied Mathematics, Vol. 11, No. 2 | 13 July Mathematical Vol. No. 3 | 12 March 2018 Cross Ref Mathematical Vol. 69, No. 5 | 12 March 2018 Cross Ref Note on of of N. E. of the for and Applied Mathematics, Vol. No. 1 | 10 July Method for Nonlinear Part Linear of the for and Applied Mathematics, Vol. No. 1 | 10 July 2, January July for and Applied for and Applied Mathematics