{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-sherman-morrison-woodbury-approach-to","title":"A Sherman--Morrison--Woodbury approach to solving least squares problems with low-rank updates","arxiv_id":"2406.15120","date":"2024-06-21","proceeding":null,"authors":["Stefan Güttel","Yuji Nakatsukasa","Marcus Webb","Alban Bloor Riley"],"abstract":"We present a simple formula to update the pseudoinverse of a full-rank rectangular matrix that undergoes a low-rank modification, and demonstrate its utility for solving least squares problems. The resulting algorithm can be dramatically faster than solving the modified least squares problem from scratch, just like the speedup enabled by Sherman--Morrison--Woodbury for solving linear systems with low-rank modifications.","url_abs":"https://arxiv.org/abs/2406.15120v2","url_pdf":"https://arxiv.org/pdf/2406.15120v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-sherman-morrison-woodbury-approach-to","repo_url":"https://github.com/nla-group/WoodburyLS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}