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A Note on the Stability of Solving a Rank-p Modification of a Linear System by the Sherman–Morrison–Woodbury Formula

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E. L. YipAuthors Info & Claims

SIAM Journal on Scientific and Statistical Computing, Volume 7, Issue 2

Pages 507 - 513

https://doi.org/10.1137/0907034

Published: 01 April 1986 Publication History

Abstract

In this paper, we address the stability of the Sherman–Morrison–Woodbury formula. Our main result states that if the original matrices, A and B, are well conditioned, then there exists matrices U and V such that the Sherman–Morrison–Woodbury formula is stable when applied to $A = B - UV^T $.

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Lindquist NLuszczek PDongarra JGallivan KNikolopoulos DBeivide RGallopoulos E(2023)Using Additive Modifications in LU Factorization Instead of PivotingProceedings of the 37th International Conference on Supercomputing10.1145/3577193.3593731(14-24)Online publication date: 21-Jun-2023
https://dl.acm.org/doi/10.1145/3577193.3593731
Fan HWeng PChu E(2022)Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencilsBIT10.1007/s10543-014-0469-154:1(147-169)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-014-0469-1
Zhang YGillman AVeerapaneni S(2022)A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulationsAdvances in Computational Mathematics10.1007/s10444-022-09974-y48:5Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10444-022-09974-y
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A Note on the Stability of Solving a Rank-p Modification of a Linear System by the Sherman–Morrison–Woodbury Formula
1. Mathematics of computing
  1. Mathematical analysis

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cover image SIAM Journal on Scientific and Statistical Computing

SIAM Journal on Scientific and Statistical Computing Volume 7, Issue 2

1986

355 pages

ISSN:0196-5204

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Society for Industrial and Applied Mathematics

United States

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Published: 01 April 1986

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Lindquist NLuszczek PDongarra JGallivan KNikolopoulos DBeivide RGallopoulos E(2023)Using Additive Modifications in LU Factorization Instead of PivotingProceedings of the 37th International Conference on Supercomputing10.1145/3577193.3593731(14-24)Online publication date: 21-Jun-2023
https://dl.acm.org/doi/10.1145/3577193.3593731
Fan HWeng PChu E(2022)Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencilsBIT10.1007/s10543-014-0469-154:1(147-169)Online publication date: 11-Mar-2022
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Hou CZhou Z(2018)One-Pass Learning with Incremental and Decremental FeaturesIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2017.276904740:11(2776-2792)Online publication date: 1-Nov-2018
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Zhang RLavaei J(2017)Modified interior-point method for large-and-sparse low-rank semidefinite programs2017 IEEE 56th Annual Conference on Decision and Control (CDC)10.1109/CDC.2017.8264510(5640-5647)Online publication date: 12-Dec-2017
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Fan HChu E(2017)Projected nonsymmetric algebraic Riccati equations and refining estimates of invariant and deflating subspacesJournal of Computational and Applied Mathematics10.1016/j.cam.2016.10.018315:C(70-86)Online publication date: 1-May-2017
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Prud'homme CPatera A(2004)Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equationsComputing and Visualization in Science10.5555/2932434.30490866:2-3(147-162)Online publication date: 1-Mar-2004
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Prud'homme CPatera A(2004)Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equationsComputing and Visualization in Science10.1007/BF026630446:2-3(147-162)Online publication date: 1-Mar-2004
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