{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:34:53Z","timestamp":1787330093163,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In this paper we present a class of robust and fully algebraic two-level preconditioners for symmetric positive definite (SPD) matrices. We introduce the notion of algebraic local symmetric positive semidefinite splitting of an SPD matrix and we give a characterization of this splitting. This splitting leads to construct algebraically and locally a class of efficient coarse spaces which bound the spectral condition number of the preconditioned system by a number defined a priori. We also introduce the $\\tau$-filtering subspace. This concept helps compare the dimension minimality of coarse spaces. Some PDEs-dependant preconditioners correspond to a special case. The examples of the algebraic coarse spaces in this paper are not practical due to expensive construction. We propose a heuristic approximation that is not costly. Numerical experiments illustrate the efficiency of the proposed method.<\/jats:p>","DOI":"10.1137\/18m1194365","type":"journal-article","created":{"date-parts":[[2019,1,15]],"date-time":"2019-01-15T14:48:55Z","timestamp":1547563735000},"page":"66-91","source":"Crossref","is-referenced-by-count":11,"title":["A Class of Efficient Locally Constructed Preconditioners Based on Coarse Spaces"],"prefix":"10.1137","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9355-4042","authenticated-orcid":true,"given":"Hussam","family":"Al Daas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura","family":"Grigori","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,1,15]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.512"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002427"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"V. Dolean, P. Jolivet, and F. Nataf,\n                      An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation\n                      , SIAM, Philadelphia, 2015,https:\/\/epubs.siam.org\/doi\/10.1137\/1.9781611974065.","DOI":"10.1137\/1.9781611974065"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050115"},{"key":"atypb5","unstructured":"L. Grigori, S. Moufawad, and F. Nataf,\n                      Enlarged Krylov Subspace Conjugate Gradient Methods for Reducing Communication\n                      , Research report RR-8597, INRIA, 2014,https:\/\/hal.inria.fr\/hal-01065985."},{"key":"atypb6","unstructured":"L. Grigori, F. Nataf, and S. Yousef,\n                      Robust Algebraic Schur Complement Preconditioners Based on Low Rank Corrections\n                      , Research report RR-8557, INRIA, 2014,https:\/\/hal.inria.fr\/hal-01017448."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1515\/jnum-2012-0013"},{"key":"atypb8","first-page":"409","volume":"49","author":"Hestenes M. R.","year":"1952","journal-title":"S.)"},{"key":"atypb9","unstructured":"X. J.\n                      Theory of Multilevel Methods\n                      , Ph.D. thesis, Cornell University, Ithaca, NY, 1989."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1997.1404"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/16M110486X"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/100796376"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1515\/rnam.1991.6.3.223"},{"key":"atypb14","first-page":"62","author":"Nepomnyaschikh S. V.","year":"1992","journal-title":"Philadelphia"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-010-0298-3"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"Y. Saad,\n                      Iterative Methods for Sparse Linear Systems\n                      , 2nd ed., SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-013-0576-y"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4534"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479800371529"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-009-9272-6"},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"A. Toselli and O. Widlund,\n                      Domain Decomposition Methods-Algorithms and Theory\n                      , Springer Ser. Comput. Math., Springer, Berlin, 2005.","DOI":"10.1007\/b137868"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1194365","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:47:20Z","timestamp":1787327240000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1194365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1194365"],"URL":"https:\/\/doi.org\/10.1137\/18m1194365","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}