{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:34:43Z","timestamp":1753886083814,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,11,24]],"date-time":"2009-11-24T00:00:00Z","timestamp":1259020800000},"content-version":"vor","delay-in-days":327,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>The approximate inverse (AINV) and the factored approximate inverse (FAPINV)\nare two known algorithms in the field of preconditioning of linear systems of equations. Both of these algorithms compute a sparse approximate inverse of matrix <jats:italic>A<\/jats:italic> in the factored form and are based on computing two sets of vectors which are <jats:italic>A<\/jats:italic>\u2010biconjugate. The AINV algorithm computes the inverse factors <jats:italic>W<\/jats:italic> and <jats:italic>Z<\/jats:italic> of a matrix independently of each other, as opposed to the AINV algorithm, where the computations of the inverse factors are done independently. In this paper, we show that, without any dropping, removing the\ndependence of the computations of the inverse factors in the FAPINV algorithm results in the AINV algorithm.<\/jats:p>","DOI":"10.1155\/2009\/179481","type":"journal-article","created":{"date-parts":[[2009,11,24]],"date-time":"2009-11-24T15:30:40Z","timestamp":1259076640000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Relation between the AINV and the FAPINV Algorithms"],"prefix":"10.1155","volume":"2009","author":[{"given":"Davod","family":"Khojasteh Salkuyeh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hadi","family":"Roohani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2009,11,24]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1137\/0907058","article-title":"GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems","volume":"20","author":"Saad Y.","year":"1986","journal-title":"SIAM Journal on Scientific and Statistical Computing"},{"volume-title":"Iterative Methods for Sparse Linear Systems","year":"1995","author":"Saad Y.","key":"e_1_2_6_2_2"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0913035"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7176"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(98)00118-4"},{"key":"e_1_2_6_6_2","unstructured":"LeeE.-J.andZhangJ. A two-phase preconditioning strategy of sparse approximate inverse for indefinite matrices 2007 no. 476-07 Department of Computer Science University of Kentuky Lexington Ky USA."},{"key":"e_1_2_6_7_2","unstructured":"LeeE.-J.andZhangJ. Factored approximate inverse preonditioners with dynamic sparsity patterns 2007 no. 488-07 Department of Computer Science University of Kentuky Lexington Ky USA."},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(93)90224-J"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(93)90252-Q"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0093-6413(92)90060-N"},{"key":"e_1_2_6_11_2","unstructured":"ZhangJ. A procedure for computing factored approximate inverse M.S. dissertation 1999 Department of Computer Science University of Kentucky Lexington Ky USA."},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00069-8"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595294691"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02512364"},{"key":"e_1_2_6_15_2","unstructured":"SalkuyehD. K. ILU preconditioning based on the FAPINV algorithm submitted."}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2009\/179481.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2009\/179481.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2009\/179481","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T14:56:06Z","timestamp":1719068166000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2009\/179481"}},"subtitle":[],"editor":[{"given":"Victor","family":"Nistor","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1155\/2009\/179481"],"URL":"https:\/\/doi.org\/10.1155\/2009\/179481","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2009,1]]},"assertion":[{"value":"2009-07-26","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-11-03","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-11-24","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"179481"}}