Some Applications of the Pseudoinverse of a Matrix

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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 Cross Ref Representations and geometrical properties of generalized inverses over fieldsLinear and Multilinear Algebra, Vol. 69 | 7 October 2021 Cross Ref Representations and symbolic computation of generalized inverses over fieldsApplied Mathematics and Computation, Vol. 406 | 1 Oct 2021 Cross Ref Fast inversion of gravimetric profiles via a modified version of the Pereyra–Rosen algorithmJournal of Earth System Science, Vol. 130, No. 3 | 4 September 2021 Cross Ref Efficient projection onto the intersection of a