A Note on the Stability of the Sherman-Morrison-Woodbury Formula
Numerical Analysis
2025-04-08 v1 Numerical Analysis
Abstract
We study the numerical stability of the Sherman-Morrison-Woodbury (SMW) identity. Let and assume and 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.
Cite
@article{arxiv.2504.04554,
title = {A Note on the Stability of the Sherman-Morrison-Woodbury Formula},
author = {Linkai Ma and Christos Boutsikas and Mehrdad Ghadiri and Petros Drineas},
journal= {arXiv preprint arXiv:2504.04554},
year = {2025}
}