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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. (English) Zbl 0628.65020
Author’s summary: We address the stability of the Sherman-Morrison- Woodbury formula [cf. G. W. Stewart, Math. Comput. 28, 537-542 (1974; Zbl 0293.65015)]. Our main result states that if the original matrices, A and B, are well conditioned, then there exist matrices U and V such that the Sherman-Morrison-Woodbury formula is stable when applied to \(A=B-UV^ T\).
Reviewer: F.Móricz

MSC:
65F05 Direct numerical methods for linear systems and matrix inversion
65F35 Numerical computation of matrix norms, conditioning, scaling
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