A Note on the Stability of the Sherman-Morrison-Woodbury Formula
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915231469404160 |
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| author | Ma, Linkai Boutsikas, Christos Ghadiri, Mehrdad Drineas, Petros |
| author_facet | Ma, Linkai Boutsikas, Christos Ghadiri, Mehrdad Drineas, Petros |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on the Stability of the Sherman-Morrison-Woodbury Formula Ma, Linkai Boutsikas, Christos Ghadiri, Mehrdad Drineas, Petros Numerical Analysis 65F05, 65F35, 15A23, 15A24, 15A45 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. |
| title | A Note on the Stability of the Sherman-Morrison-Woodbury Formula |
| topic | Numerical Analysis 65F05, 65F35, 15A23, 15A24, 15A45 |
| url | https://arxiv.org/abs/2504.04554 |