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Math. Softw."],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>\n            We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess and then performs one-sided Jacobi rotations in the working precision as iterative refinement. By carefully transforming a lower precision solution to a higher precision one, our algorithm achieves about\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(2\\times\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            speedup on the x86-64 architecture compared to the usual one-sided Jacobi SVD algorithm in LAPACK, without sacrificing the accuracy.\n          <\/jats:p>","DOI":"10.1145\/3721124","type":"journal-article","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T15:43:17Z","timestamp":1741102997000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["A Mixed Precision Jacobi SVD Algorithm"],"prefix":"10.1145","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-6675-8754","authenticated-orcid":false,"given":"Weiguo","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences and School of Data Science, Fudan University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2860-0134","authenticated-orcid":false,"given":"Yuxin","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4914-7666","authenticated-orcid":false,"given":"Meiyue","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Data Science and MOE Key Laboratory for Computational Physical Sciences, Fudan University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,4,4]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1177\/10943420211003313"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492916000015"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-43229-4_47"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-022-01327-6"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01436084"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/17M1140819"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/20M1316822"},{"key":"e_1_3_3_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/22M1487709"},{"key":"e_1_3_3_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(83)90171-3"},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/PL00005447"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022384216930"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/0910023"},{"key":"e_1_3_3_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0613074"},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","DOI":"10.5555\/264989"},{"key":"e_1_3_3_16_2","doi-asserted-by":"publisher","DOI":"10.1145\/1377612.1377616"},{"key":"e_1_3_3_17_2","doi-asserted-by":"publisher","DOI":"10.1145\/3061709"},{"key":"e_1_3_3_18_2","doi-asserted-by":"publisher","DOI":"10.1137\/050639193"},{"key":"e_1_3_3_19_2","doi-asserted-by":"publisher","DOI":"10.1137\/05063920X"},{"key":"e_1_3_3_20_2","doi-asserted-by":"publisher","DOI":"10.1137\/0106008"},{"key":"e_1_3_3_21_2","volume-title":"Library for Double\u2013Double and Quad\u2013Double Arithmetic","author":"Hida Yozo","year":"2008","unstructured":"Yozo Hida, Xiaoye S. 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