{"id":"https://openalex.org/W2088113364","doi":"https://doi.org/10.1137/140961912","title":"Block GMRES Method with Inexact Breakdowns and Deflated Restarting","display_name":"Block GMRES Method with Inexact Breakdowns and Deflated Restarting","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2088113364","doi":"https://doi.org/10.1137/140961912","mag":"2088113364"},"language":"en","primary_location":{"id":"doi:10.1137/140961912","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140961912","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-00963704","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074132178","display_name":"Emmanuel Agullo","orcid":"https://orcid.org/0000-0003-0655-6934"},"institutions":[{"id":"https://openalex.org/I86122600","display_name":"Numerical Algorithms Group (United Kingdom)","ror":"https://ror.org/04pcnys31","country_code":"GB","type":"company","lineage":["https://openalex.org/I86122600"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"E. Agullo","raw_affiliation_strings":["High-End Parallel Algorithms for Challenging Numerical Simulations"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"High-End Parallel Algorithms for Challenging Numerical Simulations","institution_ids":["https://openalex.org/I86122600"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060047917","display_name":"Luc Giraud","orcid":"https://orcid.org/0000-0002-7062-7672"},"institutions":[{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I86122600","display_name":"Numerical Algorithms Group (United Kingdom)","ror":"https://ror.org/04pcnys31","country_code":"GB","type":"company","lineage":["https://openalex.org/I86122600"]}],"countries":["FR","GB"],"is_corresponding":false,"raw_author_name":"L. Giraud","raw_affiliation_strings":["Laboratoire Bordelais de Recherche en Informatique","High-End Parallel Algorithms for Challenging Numerical Simulations"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Bordelais de Recherche en Informatique","institution_ids":["https://openalex.org/I4210142254"]},{"raw_affiliation_string":"High-End Parallel Algorithms for Challenging Numerical Simulations","institution_ids":["https://openalex.org/I86122600"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056265105","display_name":"Yan\u2010Fei Jing","orcid":"https://orcid.org/0000-0002-6120-9583"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Y.-F. Jing","raw_affiliation_strings":["School of Mathematical Sciences/Institute of Computational Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences/Institute of Computational Science","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4295,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.82668406,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"35","issue":"4","first_page":"1625","last_page":"1651"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.9247515201568604},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.7547093629837036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.723415732383728},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5875625014305115},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5696548819541931},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5566156506538391},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.522501528263092},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.45400309562683105},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3794814646244049},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.32754814624786377},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16193288564682007},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08528867363929749},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0671553909778595}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.9247515201568604},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.7547093629837036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.723415732383728},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5875625014305115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5696548819541931},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5566156506538391},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.522501528263092},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.45400309562683105},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3794814646244049},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.32754814624786377},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16193288564682007},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08528867363929749},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0671553909778595}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140961912","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140961912","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00963704v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00963704","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-8503, INRIA. 2014, pp.31","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:oai:HAL:hal-01067159v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01067159","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://epubs.siam.org/doi/abs/10.1137/140961912","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00963704v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00963704","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-8503, INRIA. 2014, pp.31","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1659539761","https://openalex.org/W1970821534","https://openalex.org/W1975714268","https://openalex.org/W1977847746","https://openalex.org/W1981908221","https://openalex.org/W1987710178","https://openalex.org/W1990033625","https://openalex.org/W1990351032","https://openalex.org/W1998574793","https://openalex.org/W2013798243","https://openalex.org/W2015805170","https://openalex.org/W2018784891","https://openalex.org/W2021037468","https://openalex.org/W2028499533","https://openalex.org/W2035080386","https://openalex.org/W2036735300","https://openalex.org/W2037714220","https://openalex.org/W2040388588","https://openalex.org/W2046160677","https://openalex.org/W2048100126","https://openalex.org/W2051133095","https://openalex.org/W2052579356","https://openalex.org/W2062477148","https://openalex.org/W2066349733","https://openalex.org/W2067028470","https://openalex.org/W2069569758","https://openalex.org/W2070376917","https://openalex.org/W2076556622","https://openalex.org/W2081696668","https://openalex.org/W2085551594","https://openalex.org/W2086160340","https://openalex.org/W2092886819","https://openalex.org/W2094624803","https://openalex.org/W2095041371","https://openalex.org/W2128573164","https://openalex.org/W2128836543","https://openalex.org/W2130901049","https://openalex.org/W2145097673","https://openalex.org/W2147542748","https://openalex.org/W2170486042","https://openalex.org/W3098036980"],"related_works":["https://openalex.org/W2032899988","https://openalex.org/W2072568196","https://openalex.org/W2971922054","https://openalex.org/W2610002741","https://openalex.org/W4220970845","https://openalex.org/W1579526657","https://openalex.org/W2522245970","https://openalex.org/W4247704229","https://openalex.org/W582364689","https://openalex.org/W4225411471"],"abstract_inverted_index":{"We":[0,17],"consider":[1],"the":[2,25,34,41,69,76,96,101],"solution":[3],"of":[4,27,43,105],"large":[5],"linear":[6],"systems":[7],"with":[8],"multiple":[9],"right-hand":[10],"sides":[11],"using":[12],"a":[13,19],"block":[14,31,35],"GMRES":[15],"approach.":[16],"introduce":[18],"new":[20,97],"algorithm":[21,55,98],"that":[22,39,95],"effectively":[23],"handles":[24],"situation":[26],"almost":[28],"rank":[29],"deficient":[30],"generated":[32],"by":[33,57,74,81],"Arnoldi":[36],"procedure":[37],"and":[38,59,109],"enables":[40],"recycling":[42],"spectral":[44],"information":[45],"at":[46],"restart.":[47],"The":[48],"first":[49],"feature":[50],"is":[51,72],"inherited":[52],"from":[53],"an":[54],"introduced":[56],"Robb\u00e9":[58],"Sadkane":[60],"[Linear":[61],"Algebra":[62],"Appl.,":[63],"419":[64],"(2006),":[65],"pp.":[66,88],"265--285],":[67],"while":[68],"second":[70],"one":[71],"obtained":[73],"extending":[75],"deflated":[77],"restarting":[78],"strategy":[79],"proposed":[80],"Morgan":[82],"[Appl.":[83],"Numer.":[84],"Math.,":[85],"54":[86],"(2005),":[87],"222--236].":[89],"Through":[90],"numerical":[91,103],"experiments,":[92],"we":[93],"show":[94],"combines":[99],"efficiently":[100],"attractive":[102],"features":[104],"its":[106],"two":[107],"parents":[108],"outperforms":[110],"them.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2016,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
