Hager, William W. Updating the inverse of a matrix. (English) Zbl 0671.65018 SIAM Rev. 31, No. 2, 221-239 (1989). The history of the formulas for updating the inverse of a matrix after a small rank perturbation to the original matrix, is presented. The relationship to the well known Schur complement is pointed out. Important applications are discussed, e.g., in least squares estimation, networks and structures (modification of a base solution), asymptotic analysis, sensitivity analysis in analysis in linear programming, domain decomposition techniques in partial differential equations, tearing and mending, quasi-Newton methods, and updating a factorization. Reviewer: R.P.Tewarson Cited in 151 Documents MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 15A09 Theory of matrix inversion and generalized inverses 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 65-03 History of numerical analysis Keywords:matrix inversion; Sherman-Morrison-Woodbury formulas; small rank perturbation; Schur complement; least squares estimation; networks; asymptotic analysis; sensitivity analysis; analysis; linear programming; domain decomposition; tearing and mending; quasi-Newton methods; updating; factorization PDFBibTeX XMLCite \textit{W. W. Hager}, SIAM Rev. 31, No. 2, 221--239 (1989; Zbl 0671.65018) Full Text: DOI Link