On the Continuity of the Generalized Inverse

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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. 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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 treesProbability Theory and Related Fields, Vol. 12 | 22 June 2021 Cross Ref Representations for the weak group inverseApplied Mathematics and Computation, Vol. 397 | 1 May 2021 Cross Ref Continuity of the core-EP inverse and its applicationsLinear and Multilinear Algebra, Vol. 69, No. 3 | 24 April 2019 Cross Ref Matrix Completion with Deterministic Sampling: Theories and MethodsIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 43, No. 2 | 1 Feb 2021 Cross Ref Perturbation Analysis of Singular Semidefinite Programs and Its Applications to Control ProblemsJournal of Optimization Theory and Applications, Vol. 188, No. 1 | 18 November 2020 Cross Ref Perturbation bounds for the W-weighted core-EP inverseJournal of Algebra and Its Applications, Vol. 19, No. 12 | 4 December 2019 Cross Ref A Simple Asymptotically F -Distributed Portmanteau Test for Diagnostic Checking of Time Series Models With Uncorrelated InnovationsJournal of Business & Economic Statistics, Vol. 15 | 25 November 2020 Cross Ref On an improved convergence analysis of a two-step Gauss-Newton type method under generalized Lipschitz conditionsCarpathian Journal of Mathematics, Vol. 36, No. 3 | 30 September 2020 Cross Ref On accurate error estimates for the quaternion least squares and weighted least squares problemsInternational Journal of Computer Mathematics, Vol. 97, No. 8 | 18 July 2019 Cross Ref Efficient GMM estimation with singular system of moment conditionsStatistical Theory and Related Fields, Vol. 4, No. 2 | 23 August 2019 Cross Ref On the perturbation of the Moore–Penrose inverse of a matrixApplied Mathematics and Computation, Vol. 374 | 1 Jun 2020 Cross Ref On the continuity and differentiability of the (dual) core inverse in C *-algebrasLinear and Multilinear Algebra, Vol. 68, No. 4 | 12 September 2018 Cross Ref Exploring implicit spaces for constrained sampling-based planningThe International Journal of Robotics Research, Vol. 38, No. 10-11 | 26 August 2019 Cross Ref Recovery map for fermionic Gaussian channelsJournal of Mathematical Physics, Vol. 60, No. 7 | 1 Jul 2019 Cross Ref BibliographyMatrix Differential Calculus with Applications in Statistics and Econometrics | 11 May 2019 Cross Ref Detection of block-exchangeable structure in large-scale correlation matricesJournal of Multivariate Analysis, Vol. 169 | 1 Jan 2019 Cross Ref Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose InverseGeneralized Inverses: Theory and Computations | 13 May 2018 Cross Ref Expanding the Applicability of Four Iterative Methods for Solving Least Squares ProblemsAnnals of West University of Timisoara - Mathematics and Computer Science, Vol. 55, No. 2 | 29 December 2017 Cross Ref Optimization of Mixed-ADC Multi-Antenna Systems for Cloud-RAN DeploymentsIEEE Transactions on Communications, Vol. 65, No. 9 | 1 Sep 2017 Cross Ref Chapter 8. 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