{"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/fast-computation-of-moore-penrose-inverse","title":"Fast Computation of Moore-Penrose Inverse Matrices","arxiv_id":"0804.4809","date":"2008-04-30","proceeding":null,"authors":["Pierre Courrieu"],"abstract":"Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors of synaptic weights, which contribute to the regularization of the input-output mapping. It is thus of interest to develop fast and accurate algorithms for computing Moore-Penrose inverse matrices. In this paper, an algorithm based on a full rank Cholesky factorization is proposed. The resulting pseudoinverse matrices are similar to those provided by other algorithms. However the computation time is substantially shorter, particularly for large systems.","url_abs":"https://arxiv.org/abs/0804.4809v1","url_pdf":"https://arxiv.org/pdf/0804.4809v1.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":"fast-computation-of-moore-penrose-inverse","repo_url":"https://github.com/FerryYoungFan/NaiveMatrixLib","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=0804.4809","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}