{"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/butterfly-factorization-via-randomized-matrix","title":"Butterfly factorization via randomized matrix-vector multiplications","arxiv_id":"2002.03400","date":"2020-02-09","proceeding":null,"authors":["Yang Liu","Xin Xing","Han Guo","Eric Michielssen","Pieter Ghysels","Xiaoye Sherry Li"],"abstract":"This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\\times n$ matrix with $m\\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The resulting factorization is composed of $O(\\log n)$ sparse factors, each containing $O(n)$ nonzero entries. The factorization can be attained using $O(n^{3/2}\\log n)$ computation and $O(n\\log n)$ memory resources. The proposed algorithm applies to matrices with strong and weak admissibility conditions arising from surface integral equation solvers with a rigorous error bound, and is implemented in parallel.","url_abs":"https://arxiv.org/abs/2002.03400v1","url_pdf":"https://arxiv.org/pdf/2002.03400v1.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":"butterfly-factorization-via-randomized-matrix","repo_url":"https://github.com/liuyangzhuan/ButterflyPACK","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}