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Updating the inverse of a matrix. (English) Zbl 0671.65018
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

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
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