{"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/iterative-refinement-with-low-precision","title":"Iterative Refinement with Low-Precision Posits","arxiv_id":"2408.13400","date":"2024-08-23","proceeding":null,"authors":["James Quinlan","E. Theodore L. Omtzigt"],"abstract":"This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation $Ax = b$, where $A$ is a large sparse matrix. Various scaling techniques, such as row and column equilibration, map the matrix entries to higher-density regions of machine numbers before performing the $O(n^3)$ factorization operation. Low-precision LU factorization followed by forward/backward substitution provides an initial estimate. The results demonstrate that a 16-bit posit configuration combined with equilibration produces accuracy comparable to IEEE half-precision (fp16), indicating a potential for achieving a balance between efficiency and accuracy.","url_abs":"https://arxiv.org/abs/2408.13400v2","url_pdf":"https://arxiv.org/pdf/2408.13400v2.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":"iterative-refinement-with-low-precision","repo_url":"https://github.com/stillwater-sc/universal","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":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}