{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T18:19:31Z","timestamp":1732040371322},"reference-count":36,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T00:00:00Z","timestamp":1616716800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,10]]},"abstract":"Abstract<\/jats:title>The solution of large sparse linear systems is required in many scientific fields such as computational fluid dynamics, computational electromagnetism, computational finance, etc. The computation of the solution of these systems is performed with preconditioned iterative methods, which rely on effective preconditioning schemes. A new class of approximate inverses is proposed, namely incomplete inverse matrices, which are computed using a recursive Schur complement\u2010based approach. This class of approximate inverses is based on a priori knowledge of a sparsity pattern. In order to have finer control over the density of the proposed approximate inverse, especially in the case of three\u2010dimensional problems, on\u2010the\u2010fly filtration is used, resulting in substantial reduction in the number of nonzero elements. Implementation details and analysis for computing the proposed scheme are given. Numerical results depicting the effectiveness and applicability of the proposed scheme are also provided.<\/jats:p>","DOI":"10.1002\/nla.2380","type":"journal-article","created":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T06:05:45Z","timestamp":1616738745000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Incomplete inverse matrices"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-6591-970X","authenticated-orcid":false,"given":"Christos K.","family":"Filelis\u2010Papadopoulos","sequence":"first","affiliation":[{"name":"Department of Computer Science University College Cork Cork Ireland"}]}],"member":"311","published-online":{"date-parts":[[2021,3,26]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"e_1_2_8_3_1","volume-title":"Iterative solution methods","author":"Axelsson O","year":"1996"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1680010405"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00412-X"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898341268"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(85)90214-9"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/0912035"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/0911045"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/0705045"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01931691"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/140968896"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11227-012-0825-3"},{"key":"e_1_2_8_14_1","doi-asserted-by":"crossref","unstructured":"LiR ZhangC. Efficient parallel implementations of sparse triangular solves for GPU architectures Proceedings of the 2020 SIAM Conference on Parallel Processing for Scientific Computing;2020. p. 106\u201317.","DOI":"10.1137\/1.9781611976137.10"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897319301"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(95)00182-4"},{"issue":"5","key":"e_1_2_8_17_1","first-page":"359","article-title":"Arms: an algebraic recursive multilevel solver for general sparse linear systems","volume":"9","author":"Saad Y","year":"2002","journal-title":"J Comput Appl Math"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759833913X"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1177\/109434200101500106"},{"key":"e_1_2_8_20_1","unstructured":"GroteMJ HuckleT. Effective parallel preconditioning with sparse approximate inverses. Proceedings of SIAM Conference on Parallel Processing for Scientific Computing. SIAM;1995. p. 466\u201371."},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594276552"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.1137\/0614004"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594271421"},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599356900"},{"key":"e_1_2_8_25_1","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/j.amc.2019.01.012","article-title":"A block version of left\u2010looking ainv preconditioner with one by one or two by two block pivots","volume":"350","author":"Rafiei A","year":"2019","journal-title":"Appl Math Comput"},{"key":"e_1_2_8_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2006.07.007"},{"key":"e_1_2_8_27_1","doi-asserted-by":"crossref","unstructured":"AnztH ChowE HuckleT DongarraJ. Batched generation of incomplete sparse approximate inverses on GPUs. Proceedings of the 7th Workshop on Latest Advances in Scalable Algorithms for Large\u2010Scale Systems ScalA '16. Piscataway NJ: IEEE Press;2016. p. 49\u201356.","DOI":"10.1109\/ScalA.2016.011"},{"key":"e_1_2_8_28_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219876213500849"},{"key":"e_1_2_8_29_1","doi-asserted-by":"publisher","DOI":"10.1108\/EC-12-2014-0261"},{"issue":"06","key":"e_1_2_8_30_1","first-page":"1850050","article-title":"A class of symmetric factored approximate inverses and hybrid two\u2010level solver","volume":"15","author":"Kyziropoulos PE","year":"2016","journal-title":"Int J ComputMethods"},{"key":"e_1_2_8_31_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-0887(199601)12:1<21::AID-CNM948>3.0.CO;2-K"},{"key":"e_1_2_8_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4754(87)90062-0"},{"key":"e_1_2_8_33_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899364441"},{"key":"e_1_2_8_34_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1109503"},{"key":"e_1_2_8_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2016.10.005"},{"key":"e_1_2_8_36_1","doi-asserted-by":"publisher","DOI":"10.1137\/0913035"},{"key":"e_1_2_8_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/2049662.2049670"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2380","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/nla.2380","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2380","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T23:28:50Z","timestamp":1698794930000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.2380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,26]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["10.1002\/nla.2380"],"URL":"https:\/\/doi.org\/10.1002\/nla.2380","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,26]]},"assertion":[{"value":"2019-08-02","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-08","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}