{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T07:55:05Z","timestamp":1790236505804,"version":"4.1.0"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/100005156","name":"Alexander von Humboldt-Stiftung","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005156","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004410","name":"T\u00fcrkiye Bilimsel ve Teknolojik Arastirma Kurumu","doi-asserted-by":"publisher","award":["BIDEB-2211"],"award-info":[{"award-number":["BIDEB-2211"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations. The convergence rate of the block Cimmino algorithm depends on the orthogonality among the block rows obtained by the partitioning method. The proposed method takes numerical orthogonality among block rows into account by proposing a row inner-product graph model of the coefficient matrix. In the graph partitioning formulation defined on this graph model, the partitioning objective of minimizing the cutsize directly corresponds to minimizing the sum of interblock inner products between block rows thus leading to an improvement in the eigenvalue spectrum of the iteration matrix. This in turn leads to a significant reduction in the number of iterations required for convergence. Extensive experiments conducted on a large set of matrices confirm the validity of the proposed method against a state-of-the-art method.<\/jats:p>","DOI":"10.1137\/18m1166407","type":"journal-article","created":{"date-parts":[[2018,12,13]],"date-time":"2018-12-13T10:47:32Z","timestamp":1544698052000},"page":"C827-C850","source":"Crossref","is-referenced-by-count":12,"title":["A Novel Partitioning Method for Accelerating the Block Cimmino Algorithm"],"prefix":"10.1137","volume":"40","author":[{"given":"F. Sukru","family":"Torun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Murat","family":"Manguoglu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cevdet","family":"Aykanat","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,12,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/13092589X"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2017.2656893"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899358194"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-92859-1_27"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044482106-5\/50009-0"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389335"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/0913003"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/0613012"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/0916086"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/15M104253X"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1973-0348991-3"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-40827-9_22"},{"key":"atypb13","unstructured":"R. B. Bramley,\n                      Row Projection Methods for Linear Systems\n                      , Ph.D. thesis, University of Illinois at Urbana-Champaign, Champaign, IL, 1989."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/0913010"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1109\/71.780863"},{"key":"atypb16","volume-title":"Technical report BU-CE-9915","author":"Catalyurek U. V.","year":"1999"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/BF01589408"},{"key":"atypb18","first-page":"326","volume":"9","author":"Cimmino G.","year":"1938","journal-title":"Ric Sci. Ser. II"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1145\/800195.805928"},{"key":"atypb20","first-page":"1","volume":"38","author":"Davis T. A.","year":"2011","journal-title":"ACM Trans. Math. 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H.","year":"1983"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1137\/040609458"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1145\/355791.355796"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/20.1.61"},{"key":"atypb35","first-page":"355","volume":"35","author":"Kaczmarz S.","year":"1937","journal-title":"Bull. Internat. Acad. Polonaise Sci. Lett."},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(89)90114-2"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1997.1403"},{"key":"atypb38","unstructured":"G. Karypis and V. Kumar,\n                      METIS - Serial Graph Partitioning and Fill-reducing Matrix Ordering\n                      ,http:\/\/www.cs.umn.edu\/ metis(2013)."},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1137\/050633032"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1145\/1089014.1089017"},{"key":"atypb41","volume-title":"The MathWorks Inc","year":"2015"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(80)90247-5"},{"key":"atypb43","unstructured":"D. Ruiz,\n                      Solution of Large Sparse Unsymmetric Linear Systems with a Block Iterative Method in a Multiprocessor Environment\n                      , Ph.D. thesis, Institut National Polytechnique de Toulouse, Toulouse, France, 1992."},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1016\/j.future.2003.07.011"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1145\/3004280"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389450"},{"key":"atypb47","unstructured":"M. Zenadi,\n                      M\u00e9thodes Hybrides pour la R\u00e9solution de Grands Syst\u00e8mes Lin\u00e9aires Creux sur Calculateurs Parall\u00e8les\n                      , Ph.D. thesis, \u00c9cole Doctorale Math\u00e9matiques, Informatique et T\u00e9l\u00e9communications, Toulouse, France, 2013."},{"key":"atypb48","unstructured":"M. Zenadi, D. Ruiz, and R. Guivarch,\n                      The Augmented Block Cimmino Distributed Solver\n                      .http:\/\/abcd.enseeiht.fr\/(2015)."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1166407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:25:38Z","timestamp":1787325938000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1166407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":48,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/18M1166407"],"URL":"https:\/\/doi.org\/10.1137\/18m1166407","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}