{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:27:56Z","timestamp":1787333276925,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In many situations, it has been observed that significant convergence improvements can be achieved in preconditioned Krylov subspace methods by enriching them with some spectral information. On the other hand, effective preconditioning strategies are often designed where the preconditioner varies from one step to the next so that a flexible Krylov solver is required. In this paper, we present a new numerical technique for nonsymmetric problems that combines these two features. We illustrate the numerical behavior of the new solver both on a set of small academic test examples as well as on large industrial simulation arising in wave propagation simulations.<\/jats:p>","DOI":"10.1137\/080741847","type":"journal-article","created":{"date-parts":[[2010,6,24]],"date-time":"2010-06-24T18:03:11Z","timestamp":1277402591000},"page":"1858-1878","source":"Crossref","is-referenced-by-count":51,"title":["Flexible GMRES with Deflated Restarting"],"prefix":"10.1137","volume":"32","author":[{"given":"L.","family":"Giraud","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Gratton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"X.","family":"Pinel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"X.","family":"Vasseur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,6,24]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019170609950"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"R. F. Boisvert, R. Pozo, K. Remington, R. Barrett, and J. J. Dongarra,\n                      The Matrix Market: A web resource for test matrix collections\n                      , in Quality of Numerical Software, Assessment and Enhancement, R. F. Boisvert, ed., Chapman & Hall, London, 1997, pp. 125\u2013137.","DOI":"10.1007\/978-1-5041-2940-4_9"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019113630790"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/040603917"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199701\/02)4:1<43::AID-NLA99>3.0.CO;2-Z"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898348040"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"G. Cohen,\n                      Higher-Order Numerical Methods for Transient Wave Equations\n                      , Springer-Verlag, Berlin, 2002.","DOI":"10.1007\/978-3-662-04823-8"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999330379"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6451"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1080\/00207160701356076"},{"key":"R11","unstructured":"I. S. Duff, R. G. Grimes, and J. G. Lewis,\n                      Users' Guide for the Harwell-Boeing Sparse Matrix Collection (Release\n                      I), Tech. report TR\/PA\/92\/86, CERFACS, Toulouse, France, 1992."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2007.01.005"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90140-9"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479893253975"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599364659"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897321362"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1680020205"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/050630416"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500381239"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/040607277"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/060656127"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/0914028"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895294289"},{"key":"R24","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":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199607\/08)3:4<329::AID-NLA86>3.0.CO;2-8"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1002\/nla.499"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894270427"},{"key":"R29","unstructured":"B. F. Smith, P. E. Bj\u00f8rstad, and W. D. Gropp,\n                      Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations\n                      , Cambridge University Press, Cambridge, UK, 1996."},{"key":"R30","unstructured":"G. Sylvand,\n                      La M\u00e9thode Multip\u00f4le Rapide en Electromagn\u00e9tisme: Performances, Parall\u00e9lisation, Applications\n                      , Ph.D. thesis, \u00c9cole Nationale des Ponts et Chauss\u00e9es, Paris, 2002."},{"key":"R31","doi-asserted-by":"crossref","unstructured":"A. Toselli and O. Widlund,\n                      Domain Decomposition Methods\u2014Algorithms and Theory\n                      , Springer Ser. Comput. Math. 34, Springer-Verlag, Berlin, 2004.","DOI":"10.1007\/b137868"},{"key":"R32","unstructured":"U. Trottenberg, C. W. Oosterlee, and A. Sch\u00fcller,\n                      Multigrid\n                      , Academic Press, San Diego, CA, 2001."},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1680010404"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080741847","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:47:11Z","timestamp":1787330831000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080741847"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080741847"],"URL":"https:\/\/doi.org\/10.1137\/080741847","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}