{"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/accelerating-a-restarted-krylov-method-for","title":"Accelerating a restarted Krylov method for matrix functions with randomization","arxiv_id":"2503.22631","date":"2025-03-28","proceeding":null,"authors":["Nicolas L. Guidotti","Per-Gunnar Martinsson","Juan A. Acebrón","José Monteiro"],"abstract":"Many scientific applications require the evaluation of the action of a matrix function on a vector, and Krylov subspace methods are the most common ones for this task. Since the orthogonalization cost and the memory requirements can quickly become overwhelming as the basis grows, the Krylov method is often restarted after a few iterations. This paper proposes a new acceleration technique for restarted Krylov methods based on randomization. The numerical experiments show that the randomized method greatly outperforms the classical approach at the same level of accuracy. In fact, randomization can actually improve the convergence rate of restarted methods in some cases. The paper also compares the performance and stability of several existing randomized methods for solving very large, ill-conditioned problems, complementing the numerical analyses from previous studies.","url_abs":"https://arxiv.org/abs/2503.22631v3","url_pdf":"https://arxiv.org/pdf/2503.22631v3.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":"accelerating-a-restarted-krylov-method-for","repo_url":"https://gitlab.com/nlg550/randomized-krylov","is_official":1,"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}