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arXiv · 2504.04554

A Note on the Stability of the Sherman-Morrison-Woodbury Formula

Linkai Ma·Christos Boutsikas·Mehrdad Ghadiri·Petros Drineas
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Abstract

We study the numerical stability of the Sherman-Morrison-Woodbury (SMW) identity. Let $B = A + UV^T$ and assume $U$ and $V$ both have full-column rank. We explore error bounds for the SMW identity when we are only able to compute approximate inverses. For both forward and backward errors, we present upper bounds as a function of the two-norm error of the approximate inverses. We verify with numerical experiments that, in certain cases, our bounds accurately capture the behavior of the errors.

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Linkai Ma, Christos Boutsikas, Mehrdad Ghadiri, Petros Drineas. 2025-04-06. A Note on the Stability of the Sherman-Morrison-Woodbury Formula. https://arxiv.org/abs/2504.04554

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