{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:43:06Z","timestamp":1787330586595,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001700","name":"Japanese Ministry of Education, Science, Sports and Culture","doi-asserted-by":"crossref","award":["26286087"],"award-info":[{"award-number":["26286087"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001700","name":"Japanese Ministry of Education, Science, Sports and Culture","doi-asserted-by":"crossref","award":["16KT0016"],"award-info":[{"award-number":["16KT0016"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001700","name":"Japanese Ministry of Education, Science, Sports and Culture","doi-asserted-by":"crossref","award":["17H02828"],"award-info":[{"award-number":["17H02828"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100006109","name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","doi-asserted-by":"publisher","award":["2\/0004\/17"],"award-info":[{"award-number":["2\/0004\/17"]}],"id":[{"id":"10.13039\/501100006109","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We present a proof of the global and asymptotic quadratic convergence of the serial and parallel two-sided block-Jacobi SVD algorithm with dynamic ordering. In the serial case, one pair of the off-diagonal blocks with the largest weight given as the sum of squares of Frobenius norms is annihilated. In the parallel case, using the greedy implementation of dynamic ordering and having $p$ processors, $p$ pairs of the off-diagonal blocks with largest weights, and disjoint block row and column indices are annihilated in each parallel iteration step. Additionally, the asymptotic quadratic convergence is also proved for the scaled iterated matrix, both in serial and parallel cases. Numerical examples confirm the developed theory.<\/jats:p>","DOI":"10.1137\/18m1222727","type":"journal-article","created":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T14:29:38Z","timestamp":1558621778000},"page":"639-671","source":"Crossref","is-referenced-by-count":6,"title":["Asymptotic Quadratic Convergence of the Two-Sided Serial and Parallel Block-Jacobi SVD Algorithm"],"prefix":"10.1137","volume":"40","author":[{"given":"Gabriel","family":"Ok\u0161a","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yusaku","family":"Yamamoto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Be\u010dka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mari\u00e1n","family":"Vajter\u0161ic","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,5,23]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8191(01)00138-7"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129626415500036"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-012-0388-y"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90031-0"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/0707001"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/0613074"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-009-0240-8"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/050639193"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/05063920X"},{"key":"atypb10","unstructured":"G. Golub and C. F. V. Loan,\n                      Matrix Computations\n                      , Johns Hopkins University Press, Baltimore, 2013."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385728"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-014-0647-8"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-53-02004-3"},{"key":"atypb14","first-page":"51","volume":"30","author":"C. G.","year":"1846","journal-title":"J. Reine Angew. Math."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/88795"},{"key":"atypb16","first-page":"1","volume":"29","author":"Kudo S.","year":"2017","journal-title":"Concurrency Comp. Pract. Exper."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.14495\/jsiaml.10.41"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1109\/12.24289"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989222792X"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989324820X"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-018-0711-3"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-016-0863-5"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(86)90173-4"},{"key":"atypb24","unstructured":"B. N. Parlett,\n                      The Symmetric Eigenvalue Problem\n                      , SIAM, Philadelphia, 1987."}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1222727","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:14:07Z","timestamp":1787328847000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1222727"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1222727"],"URL":"https:\/\/doi.org\/10.1137\/18m1222727","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}