{"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/updating-singular-value-decomposition-for","title":"Updating Singular Value Decomposition for Rank One Matrix Perturbation","arxiv_id":"1707.08369","date":"2017-07-26","proceeding":null,"authors":["Ratnik Gandhi","Amoli Rajgor"],"abstract":"An efficient Singular Value Decomposition (SVD) algorithm is an important\ntool for distributed and streaming computation in big data problems. It is\nobserved that update of singular vectors of a rank-1 perturbed matrix is\nsimilar to a Cauchy matrix-vector product. With this observation, in this\npaper, we present an efficient method for updating Singular Value Decomposition\nof rank-1 perturbed matrix in $O(n^2 \\ \\text{log}(\\frac{1}{\\epsilon}))$ time.\nThe method uses Fast Multipole Method (FMM) for updating singular vectors in\n$O(n \\ \\text{log} (\\frac{1}{\\epsilon}))$ time, where $\\epsilon$ is the\nprecision of computation.","url_abs":"http://arxiv.org/abs/1707.08369v1","url_pdf":"http://arxiv.org/pdf/1707.08369v1.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":"abstracts"},"code_links":[{"paper_slug":"updating-singular-value-decomposition-for","repo_url":"https://github.com/AmoliR/rank1-svd-update","is_official":0,"mentioned_in_paper":0,"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}