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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

1986; Society for Industrial and Applied Mathematics; Volume: 7; Issue: 2 Linguagem: Inglês

10.1137/0907034

2168-3417

E. L. Yip,

Polynomial and algebraic computation

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 $.