A Note on the Stability of the Sherman-Morrison-Woodbury Formula
Abstract
We study the numerical stability of the Sherman-Morrison-Woodbury (SMW) identity. Let B = A + UVT 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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