{"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/the-stability-of-split-preconditioned-fgmres","title":"The stability of split-preconditioned FGMRES in four precisions","arxiv_id":"2303.11901","date":"2023-03-21","proceeding":null,"authors":["Erin Carson","Ieva Daužickaitė"],"abstract":"We consider the split-preconditioned FGMRES method in a mixed precision framework, in which four potentially different precisions can be used for computations with the coefficient matrix, application of the left preconditioner, application of the right preconditioner, and the working precision. Our analysis is applicable to general preconditioners. We obtain bounds on the backward and forward errors in split-preconditioned FGMRES. Our analysis further provides insight into how the various precisions should be chosen; under certain assumptions, a suitable selection guarantees a backward error on the order of the working precision.","url_abs":"https://arxiv.org/abs/2303.11901v2","url_pdf":"https://arxiv.org/pdf/2303.11901v2.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":"the-stability-of-split-preconditioned-fgmres","repo_url":"https://github.com/dauzickaite/mpfgmres","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}