On the Continuity of the Generalized Inverse

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 SectionsAbout1 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 Scholar2 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 Scholar3 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 Scholar4 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 Scholar5 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 Scholar6 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 Scholar7 Alston S. Householder, Unitary triangularization of a nonsymmetric matrix, J. Assoc. Comput. Mach. , 5 (1958), 339–342 MR0111128 (22: 1992) 0121. 33802 CrossrefISIGoogle Scholar8 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 Scholar9 E. H. Moors, On the reciprocal of the general algebraic matrix, Bull. Amer. Math. Soc. , 26 (1919-20), 394–395, Abstract Google Scholar10 R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. , 51 (1955), 406–413 MR0069793 (16, 1082a) 0065. 24603 CrossrefGoogle Scholar11 R. Penrose, On best approximation solutions of linear matrix equations, Proc. Cambridge Philos. Soc. , 52 (1956), 17–19 MR0074092 (17, 536d) CrossrefGoogle Scholar12 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 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. Inexact Gauss-Newton method for least square problemsIterative Methods and Their Dynamics with Applications | 5 June 2017 Cross Ref Dynamic bit selection in mixed-ADC cloud-RAN systems2017 IEEE International Conference on Communications (ICC) | 1 May 2017 Cross Ref Condition Numbers of the Multidimensional Total Least Squares ProblemBing Zheng, Lingsheng Meng, and Yimin WeiSIAM Journal on Matrix Analysis and Applications, Vol. 38, No. 3 | 31 August 2017AbstractPDF (385 KB) Least Squares ProblemsScientific Computing | 15 May 2018 Cross Ref Hamiltonian Monte Carlo sampling in Bayesian empirical likelihood computationJournal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 79, No. 1 | 7 April 2016 Cross Ref Mixed-ADC Massive MIMO Uplink in Frequency-Selective ChannelsIEEE Transactions on Communications, Vol. 64, No. 11 | 1 Nov 2016 Cross Ref Extended Local Analysis of Inexact Gauss-Newton-like Method for Least Square Problems using Restricted Convergence DomainsAnnals of West University of Timisoara - Mathematics and Computer Science, Vol. 54, No. 1 | 24 September 2016 Cross Ref Inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant conditionNumerical Algorithms, Vol. 72, No. 2 | 9 September 2015 Cross Ref Isolating invisible dynamics in the design of robust hybrid internal modelsAutomatica, Vol. 68 | 1 Jun 2016 Cross Ref Mixed-ADC Massive MIMOIEEE Journal on Selected Areas in Communications, Vol. 34, No. 4 | 1 Apr 2016 Cross Ref Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov ProcessesEngineering Mathematics II | 11 February 2017 Cross Ref Guaranteed Ellipse Fitting with a Confidence Region and an Uncertainty Measure for Centre, Axes, and OrientationJournal of Mathematical Imaging and Vision, Vol. 52, No. 2 | 25 September 2014 Cross Ref Minimum HGR correlation principle: From marginals to joint distribution2015 IEEE International Symposium on Information Theory (ISIT) | 1 Jun 2015 Cross Ref New multiplicative perturbation bounds of the Moore–Penrose inverseLinear and Multilinear Algebra, Vol. 63, No. 5 | 3 July 2014 Cross Ref Enforcing consistency constraints in uncalibrated multiple homography estimation using latent variablesMachine Vision and Applications, Vol. 26, No. 2-3 | 13 March 2015 Cross Ref A note on multiplicative perturbation bounds for the Moore–Penrose inverseLinear and Multilinear Algebra, Vol. 62, No. 6 | 2 May 2013 Cross Ref Optimal Distributed Kalman Filtering Fusion With Singular Covariances of Filtering Errors and Measurement NoisesIEEE Transactions on Automatic Control, Vol. 59, No. 5 | 1 May 2014 Cross Ref Robust Least Squares Approach to Passive Target Localization Using Ultrasonic Receiver ArrayIEEE Transactions on Industrial Electronics, Vol. 61, No. 4 | 1 Apr 2014 Cross Ref Optimal Estimation of Free Energies and Stationary Densities from Multiple Biased SimulationsHao Wu and Frank NoéMultiscale Modeling & Simulation, Vol. 12, No. 1 | 16 January 2014AbstractPDF (458 KB) Execute Elementary Row and Column Operations on the Partitioned Matrix to Compute M-P Inverse A†Abstract and Applied Analysis, Vol. 2014 | 1 Jan 2014 Cross Ref Internal Model Principle for Linear Systems With Periodic State JumpsIEEE Transactions on Automatic Control, Vol. 58, No. 11 | 1 Nov 2013 Cross Ref Local convergence of the Gauss–Newton method for injective-overdetermined systems of equations under a majorant conditionComputers & Mathematics with Applications, Vol. 66, No. 4 | 1 Sep 2013 Cross Ref A Guass–Newton-like method for inverse eigenvalue problemsInternational Journal of Computer Mathematics, Vol. 90, No. 7 | 1 Jul 2013 Cross Ref A convergence analysis for pose graph optimization via Gauss-Newton methods2013 IEEE International Conference on Robotics and Automation | 1 May 2013 Cross Ref A note on stable perturbations of Moore-Penrose inversesNumerical Linear Algebra with Applications, Vol. 20, No. 1 | 12 December 2011 Cross Ref Strong Stability of Invariant Subspaces of Quaternion MatricesAdvances in Structured Operator Theory and Related Areas | 8 August 2013 Cross Ref Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithmMathematical Programming Computation, Vol. 4, No. 4 | 13 July 2012 Cross Ref Smoothness of generalized inversesIndagationes Mathematicae, Vol. 23, No. 4 | 1 Dec 2012 Cross Ref Hybrid internal models for robust spline tracking2012 IEEE 51st IEEE Conference on Decision and Control (CDC) | 1 Dec 2012 Cross Ref Convergence analysis of a proximal Gauss-Newton methodComputational Optimization and Applications, Vol. 53, No. 2 | 27 March 2012 Cross Ref Stability of Invariant Subspaces of Quaternion MatricesComplex Analysis and Operator Theory, Vol. 6, No. 5 | 28 March 2012 Cross Ref Change-point analysis in increasing dimensionJournal of Multivariate Analysis, Vol. 111 | 1 Oct 2012 Cross Ref Smoothness of generalized inversesIndagationes Mathematicae, Vol. 23, No. 3 | 1 Sep 2012 Cross Ref ReferencesNetworked Multisensor Decision and Estimation Fusion | 18 July 2012 Cross Ref Performance Analysis of the Robust Least Squares Target Localization Scheme using RDOA MeasurementsJournal of Electrical Engineering and Technology, Vol. 7, No. 4 | 1 Jul 2012 Cross Ref Canonical angles and limits of sequences of EP and co-EP matricesApplied Mathematics and Computation, Vol. 218, No. 17 | 1 May 2012 Cross Ref Local convergence analysis of inexact Gauss–Newton like methods under majorant conditionJournal of Computational and Applied Mathematics, Vol. 236, No. 9 | 1 Mar 2012 Cross Ref Hybrid output regulation with unmeasured clockIEEE Conference on Decision and Control and European Control Conference | 1 Dec 2011 Cross Ref Local convergence analysis of the Gauss–Newton method under a majorant conditionJournal of Complexity, Vol. 27, No. 1 | 1 Feb 2011 Cross Ref MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric SystemsSou-Cheng T. Choi, Christopher C. Paige, and Michael A. SaundersSIAM Journal on Scientific Computing, Vol. 33, No. 4 | 4 August 2011AbstractPDF (494 KB) A note about hybrid linear regulation49th IEEE Conference on Decision and Control (CDC) | 1 Dec 2010 Cross Ref A note of computation for M-P inverse A†International Journal of Computer Mathematics, Vol. 87, No. 10 | 1 Aug 2010 Cross Ref The optimal perturbation bounds of the Moore–Penrose inverse under the Frobenius normLinear Algebra and its Applications, Vol. 432, No. 4 | 1 Feb 2010 Cross Ref Papers on Least Squares, Projections, and Generalized InversesG. W. Stewart | 1 Jan 2010 Cross Ref Robustness of Stein-type estimators under a non-scalar error covariance structureJournal of Multivariate Analysis, Vol. 100, No. 10 | 1 Nov 2009 Cross Ref Approximation and continuity of Moore–Penrose inverses of orthogonal row block matricesApplied Mathematics and Computation, Vol. 210, No. 1 | 1 Apr 2009 Cross Ref Minimum Variance in Biased Estimation With Singular Fisher Information MatrixIEEE Transactions on Signal Processing, Vol. 57, No. 1 | 1 Jan 2009 Cross Ref Continuity properties of the 1-inverse and perturbation bounds for the Drazin inverseLinear Algebra and its Applications, Vol. 429, No. 5-6 | 1 Sep 2008 Cross Ref Variations for the Q- and H-factors in the polar decompositionCalcolo, Vol. 45, No. 2 | 8 October 2008 Cross Ref The convergence analysis of inexact Gauss–Newton methods for nonlinear problemsComputational Optimization and Applications, Vol. 40, No. 1 | 26 October 2007 Cross Ref Majorizing Functions and Convergence of the Gauss–Newton Method for Convex Composite OptimizationChong Li and K. F. NgSIAM Journal on Optimization, Vol. 18, No. 2 | 1 August 2007AbstractPDF (286 KB) Local convergence results of Gauss–Newton's like method in weak conditionsJournal of Mathematical Analysis and Applications, Vol. 324, No. 2 | 1 Dec 2006 Cross Ref Convergence of Gauss–Newton’s method and uniqueness of the solutionApplied Mathematics and Computation, Vol. 170, No. 1 | 1 Nov 2005 Cross Ref The Basic Principles for Stable Approximations to Orthogonal Generalized Inverses of Linear Operators in Hilbert SpacesNumerical Functional Analysis and Optimization, Vol. 26, No. 6 | 1 Sep 2005 Cross Ref Convergence and uniqueness properties of Gauss-Newton's methodComputers & Mathematics with Applications, Vol. 47, No. 6-7 | 1 Mar 2004 Cross Ref Linear optimal prediction and innovations representations of hidden Markov modelsStochastic Processes and their Applications, Vol. 108, No. 1 | 1 Nov 2003 Cross Ref An improvement on perturbation bounds for the Drazin inverseNumerical Linear Algebra with Applications, Vol. 10, No. 7 | 1 January 2003 Cross Ref Variants of the Greville Formula with Applications to Exact Recursive Least SquaresJie Zhou, Yunmin Zhu, X. Rong Li, and Zhisheng YouSIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 1 | 31 July 2006AbstractPDF (168 KB) Perturbation bound of the Drazin inverseApplied Mathematics and Computation, Vol. 125, No. 2-3 | 1 Jan 2002 Cross Ref Perturbation of least squares problem in Hilbert spacesApplied Mathematics and Computation, Vol. 121, No. 2-3 | 1 Jun 2001 Cross Ref Representations for Moore-Penrose inverses in Hilbert spacesApplied Mathematics Letters, Vol. 14, No. 5 | 1 Jan 2001 Cross Ref O (n3) noniterative heuristic algorithm for linear programs with error-free implementationApplied Mathematics and Computation, Vol. 110, No. 1 | 1 Apr 2000 Cross Ref The perturbation of the Drazin inverse and oblique projectionApplied Mathematics Letters, Vol. 13, No. 3 | 1 Apr 2000 Cross Ref A direct heuristic algorithm for linear programmingProceedings Mathematical Sciences, Vol. 110, No. 1 | 1 Feb 2000 Cross Ref Perturbation bound of singular linear systemsApplied Mathematics and Computation, Vol. 105, No. 2-3 | 1 Nov 1999 Cross Ref On the perturbation of the group inverse and oblique projectionApplied Mathematics and Computation, Vol. 98, No. 1 | 1 Jan 1999 Cross Ref The perturbation theory for the Drazin inverse and its applicationsLinear Algebra and its Applications, Vol. 258 | 1 Jun 1997 Cross Ref Further Study and Generalization of Kahan’s Matrix Extension TheoremDao-Sheng ZhengSIAM Journal on Matrix Analysis and Applications, Vol. 17, No. 3 | 17 February 2012AbstractPDF (729 KB) On the perturbation of the least squares solutions in Hilbert spacesLinear Algebra and its Applications, Vol. 212-213 | 1 Nov 1994 Cross Ref Concise row-pruning algorithm to invert a matrixApplied Mathematics and Computation, Vol. 61, No. 1 | 1 Mar 1994 Cross Ref Perturbation analysis for the projection of a point to an affine setLinear Algebra and its Applications, Vol. 191 | 1 Sep 1993 Cross Ref A note on generalized wald’s methodMetrika, Vol. 37, No. 1 | 1 Dec 1990 Cross Ref Lower bounds for parametric estimation with constraintsIEEE Transactions on Information Theory, Vol. 36, No. 6 | 1 Nov 1990 Cross Ref On the matrix convexity of the moore—penrose inverse and some applicationsLinear and Multilinear Algebra, Vol. 24, No. 4 | 1 Apr 1989 Cross Ref The local convergence of ABS methods for nonlinear algebraic equationsNumerische Mathematik, Vol. 51, No. 4 | 1 Jul 1987 Cross Ref Asymptotic Results for Generalized Wald TestsEconometric Theory, Vol. 3, No. 3 | 11 February 2009 Cross Ref Generalized inverses and asymptotic properties of Wald testsEconomics Letters, Vol. 24, No. 4 | 1 Jan 1987 Cross Ref The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-modelMetrika, Vol. 32, No. 1 | 1 Dec 1985 Cross Ref Continuity properties of stationary points of quadratic functionals in hilbert spaceNumerical Functional Analysis and Optimization, Vol. 3, No. 2 | 26 June 2007 Cross Ref On rank-deficient pseudoinversesLinear Algebra and its Applications, Vol. 29 | 1 Feb 1980 Cross Ref Parametric modeling of transient electromagnetic systemsRadio Science, Vol. 14, No. 3 | 7 December 2012 Cross Ref The rank of a difference of matrices and associated generalized inversesLinear Algebra and its Applications, Vol. 24 | 1 Apr 1979 Cross Ref On the Derivative of the Drazin Inverse of a Complex MatrixRobert E. Hartwig and Jim ShoafSIAM Journal on Mathematical Analysis, Vol. 10, No. 1 | 17 February 2012AbstractPDF (907 KB) A New Nonparametric Approach to the Comparison ofK Independent Samples of Response Curves II: AK Sample Generalization of the FRIEDMAN TestBiometrical Journal, Vol. 21, No. 2 | 1 Jan 1979 Cross Ref Computer solution and perturbation analysis of generalized linear least squares problemsMathematics of Computation, Vol. 33, No. 145 | 1 January 1979 Cross Ref Fehleranalyse für die Gauß-Elimination zur Berechnung der Lösung minimaler LängeNumerische Mathematik, Vol. 30, No. 2 | 1 Jun 1978 Cross Ref Analysis of algorithms with Hessian restoration from gradient valuesCybernetics, Vol. 13, No. 5 | 1 Jan 1978 Cross Ref Calculating the best approximate solution of an operator equationMathematics of Computation, Vol. 32, No. 144 | 1 January 1978 Cross Ref On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares ProblemsG. W. StewartSIAM Review, Vol. 19, No. 4 | 17 February 2012AbstractPDF (2178 KB) On continuity of the Moore-Penrose and Drazin generalized inversesLinear Algebra and its Applications, Vol. 18, No. 1 | 1 Jan 1977 Cross Ref Differentiation of the Drazin InverseStephen L. CampbellSIAM Journal on Applied Mathematics, Vol. 30, No. 4 | 28 July 2006AbstractPDF (363 KB) Residue Arithmetic Algorithms for Exact Computation of g-Inverses of MatricesT. Mahadeva Rao, K. Subramanian, and E. V. KrishnamurthySIAM Journal on Numerical Analysis, Vol. 13, No. 2 | 14 July 2006AbstractPDF (1158 KB) Perturbations and Approximations for Generalized Inverses and Linear Operator EquationsGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Annotated Bibliography on Generalized Inverses and ApplicationsGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Continuity properties of the Drazin pseudoinverseLinear Algebra and its Applications, Vol. 10, No. 1 | 1 Feb 1975 Cross Ref On the solution of the linear least squares problems and pseudo-inversesComputing, Vol. 13, No. 3-4 | 1 Sep 1974 Cross Ref Approximations to Generalized Inverses of Linear OperatorsR. H. Moore and M. Z. NashedSIAM Journal on Applied Mathematics, Vol. 27, No. 1 | 12 July 2006AbstractPDF (1415 KB) On the Numerical Properties of an Iterative Method for Computing the Moore–Penrose Generalized InverseTorsten Söderström and G. W. StewartSIAM Journal on Numerical Analysis, Vol. 11, No. 1 | 14 July 2006AbstractPDF (1050 KB) Perturbation theory for pseudo-inversesBIT, Vol. 13, No. 2 | 1 Jun 1973 Cross Ref The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables SeparateG. H. Golub and V. PereyraSIAM Journal on Numerical Analysis, Vol. 10, No. 2 | 14 July 2006AbstractPDF (1690 KB) ReferencesRegression and the Moore-Penrose Pseudoinverse | 1 Jan 1972 Cross Ref Error analysis in a problem of approximation of a solution of perturbed signal space and its orthogonal complementProceedings of Thirtieth Southeastern Symposium on System Theory Cross Ref Extensions and applications of the Householder algorithm for solving linear least squares problemsMathematics of Computation, Vol. 23, No. 108 | 1 January 1969 Cross Ref Volume 17, Issue 1| 1969SIAM Journal on Applied Mathematics1-221 History Submitted: 26 April 1968Published online: 28 July 2006 InformationCopyright © 1969 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI: 10. 1137/0117004Article page range: pp. 33-45ISSN (print): 0036-1399ISSN (online): 1095-712XPublisher: Society for Industrial and Applied Mathematics