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Math. Softw."],"published-print":{"date-parts":[[2023,3,31]]},"abstract":"<jats:p>The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.<\/jats:p>","DOI":"10.1145\/3582493","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T13:54:51Z","timestamp":1675691691000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement"],"prefix":"10.1145","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8559-9600","authenticated-orcid":false,"given":"Patrick","family":"Amestoy","sequence":"first","affiliation":[{"name":"Mumps Technologies, ENS Lyon, Lyon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3207-7021","authenticated-orcid":false,"given":"Alfredo","family":"Buttari","sequence":"additional","affiliation":[{"name":"CNRS, IRIT, Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5956-4976","authenticated-orcid":false,"given":"Nicholas J.","family":"Higham","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Manchester, Manchester, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5804-993X","authenticated-orcid":false,"given":"Jean-Yves","family":"L\u2019Excellent","sequence":"additional","affiliation":[{"name":"Mumps Technologies, ENS Lyon, Lyon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9949-4634","authenticated-orcid":false,"given":"Theo","family":"Mary","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, CNRS, LIP6, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8429-7400","authenticated-orcid":false,"given":"Bastien","family":"Vieubl\u00e9","sequence":"additional","affiliation":[{"name":"INPT, IRIT, Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,3,21]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/130938505"},{"issue":"3","key":"e_1_3_3_3_2","first-page":"A1907\u2013A1928","article-title":"A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces","volume":"43","author":"Daas Hussam Al","year":"2021","unstructured":"Hussam Al Daas, Laura Grigori, Pierre Jolivet, and Pierre-Henri Tournier. 2021. 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