On the Continuity of the Generalized Inverse

Abstract

Previous article Next article On the Continuity of the Generalized InverseG. W. StewartG. W. Stewarthttps://doi.org/10.1137/0117004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. N. Afriat, Orthogonal and oblique projectors and the characteristics of pairs of vector spaces, Proc. Cambridge Philos. Soc., 53 (1957), 800–816 MR0094880 (20:1389) CrossrefGoogle Scholar[2] A. Ben-Israel and , A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math., 11 (1963), 667–699 10.1137/0111051 MR0179192 (31:3441) 0116.32202 LinkISIGoogle Scholar[3] Adi Ben-Israel, On error bounds for generalized inverses, SIAM J. Numer. Anal., 3 (1966), 585–592 10.1137/0703050 MR0215504 (35:6344) 0147.13201 LinkGoogle Scholar[4] G. Golub and , W. Kahan, Calculating the singular values and pseudo-inverse of a matrix, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), 205–224 MR0183105 (32:587) 0194.18201 LinkGoogle Scholar[5] G. Golub, Numerical methods for solving linear least squares problems, Numer. Math., 7 (1965), 206–216 10.1007/BF01436075 MR0181094 (31:5323) 0142.11502 CrossrefGoogle Scholar[6] G. H. Golub and , J. H. Wilkinson, Note on the iterative refinement of least squares solution, Numer. Math., 9 (1966), 139–148 10.1007/BF02166032 MR0212984 (35:3849) 0156.16106 CrossrefISIGoogle Scholar[7] Alston S. Householder, Unitary triangularization of a nonsymmetric matrix, J. Assoc. Comput. Mach., 5 (1958), 339–342 MR0111128 (22:1992) 0121.33802 CrossrefISIGoogle Scholar[8] Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964xi+257 MR0175290 (30:5475) 0161.12101 Google Scholar[9] E. H. Moors, On the reciprocal of the general algebraic matrix, Bull. Amer. Math. Soc., 26 (1919-20), 394–395, Abstract Google Scholar[10] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 (16,1082a) 0065.24603 CrossrefGoogle Scholar[11] R. Penrose, On best approximation solutions of linear matrix equations, Proc. Cambridge Philos. Soc., 52 (1956), 17–19 MR0074092 (17,536d) CrossrefGoogle Scholar[12] J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall Inc., Englewood Cliffs, N.J., 1963vi+161 MR0161456 (28:4661) 1041.65502 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Homogeneity tests for one-way models with dependent errors under correlated groupsTEST, Vol. 11 | 2 September 2022 Cross Ref Bayesian linear models for cardinal paired comparison dataComputational Statistics & Data Analysis, Vol. 172 | 1 Aug 2022 Cross Ref Blind inverse problems with isolated spikesInformation and Inference: A Journal of the IMA, Vol. 64 | 16 June 2022 Cross Ref Tension distribution algorithm based on graphics with high computational efficiency and robust optimization for two-redundant cable-driven parallel robotsMechanism and Machine Theory, Vol. 172 | 1 Jun 2022 Cross Ref Expressions and properties of weak core inverseApplied Mathematics and Computation, Vol. 415 | 1 Feb 2022 Cross Ref Acute perturbation for Moore-Penrose inverses of tensors via the T-ProductJournal of Applied Mathematics and Computing, Vol. 3 | 4 January 2022 Cross Ref Forward and inverse analysis for particle size distribution measurements of disperse samples: A reviewMeasurement, Vol. 187 | 1 Jan 2022 Cross Ref Differential-algebraic boundary-value problems with the variable rank of leading-coefficient matrixJournal of Mathematical Sciences, Vol. 259, No. 1 | 16 October 2021 Cross Ref Representations and properties for the MPCEP inverseJournal of Applied Mathematics and Computing, Vol. 67, No. 1-2 | 6 January 2021 Cross Ref Differential-algebraic boundary-value problems with the variable rank of leading-coefficient matrixUkrainian Mathematical Bulletin, Vol. 18, No. 3 | 9 September 2021 Cross Ref The local limit of uniform spanning treesProbabil