{"id":"https://openalex.org/W2051863232","doi":"https://doi.org/10.1145/1067967.1067970","title":"Algorithm 842","display_name":"Algorithm 842","publication_year":2005,"publication_date":"2005-06-01","ids":{"openalex":"https://openalex.org/W2051863232","doi":"https://doi.org/10.1145/1067967.1067970","mag":"2051863232"},"language":"en","primary_location":{"id":"doi:10.1145/1067967.1067970","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1067967.1067970","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073044597","display_name":"Val\u00e9rie Frayss\u00e9","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Val\u00e9rie Frayss\u00e9","raw_affiliation_strings":["Kvasar Technology LLC, Boston, MA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kvasar Technology LLC, Boston, MA","institution_ids":[]}]},{"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/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Luc Giraud","raw_affiliation_strings":["CERFACS, Toulouse Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERFACS, Toulouse Cedex, France","institution_ids":["https://openalex.org/I4210106946"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Serge Gratton","orcid":null},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Serge Gratton","raw_affiliation_strings":["CERFACS, Toulouse Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERFACS, Toulouse Cedex, France","institution_ids":["https://openalex.org/I4210106946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020584809","display_name":"Julien Langou","orcid":"https://orcid.org/0000-0002-7803-1822"},"institutions":[{"id":"https://openalex.org/I2802706902","display_name":"Knoxville College","ror":"https://ror.org/02bxrp522","country_code":"US","type":"education","lineage":["https://openalex.org/I2802706902"]},{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julien Langou","raw_affiliation_strings":["University of Tennessee, Knoxville, Knoxville, TN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tennessee, Knoxville, Knoxville, TN","institution_ids":["https://openalex.org/I2802706902","https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073044597"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.4819,"has_fulltext":false,"cited_by_count":122,"citation_normalized_percentile":{"value":0.99269547,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"31","issue":"2","first_page":"228","last_page":"238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.8735883235931396},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.867948591709137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7417744994163513},{"id":"https://openalex.org/keywords/software-portability","display_name":"Software portability","score":0.6700527667999268},{"id":"https://openalex.org/keywords/double-precision-floating-point-format","display_name":"Double-precision floating-point format","score":0.6202487945556641},{"id":"https://openalex.org/keywords/distributed-memory","display_name":"Distributed memory","score":0.6111088991165161},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5974863171577454},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5967035293579102},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.5689676403999329},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5451277494430542},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.4626155495643616},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4510924816131592},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42142438888549805},{"id":"https://openalex.org/keywords/shared-memory","display_name":"Shared memory","score":0.3126710057258606},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.1136225163936615}],"concepts":[{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.8735883235931396},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.867948591709137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7417744994163513},{"id":"https://openalex.org/C63000827","wikidata":"https://www.wikidata.org/wiki/Q3080428","display_name":"Software portability","level":2,"score":0.6700527667999268},{"id":"https://openalex.org/C35912277","wikidata":"https://www.wikidata.org/wiki/Q1243369","display_name":"Double-precision floating-point format","level":3,"score":0.6202487945556641},{"id":"https://openalex.org/C91481028","wikidata":"https://www.wikidata.org/wiki/Q1054686","display_name":"Distributed memory","level":3,"score":0.6111088991165161},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5974863171577454},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5967035293579102},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.5689676403999329},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5451277494430542},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.4626155495643616},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4510924816131592},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42142438888549805},{"id":"https://openalex.org/C133875982","wikidata":"https://www.wikidata.org/wiki/Q764810","display_name":"Shared memory","level":2,"score":0.3126710057258606},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.1136225163936615},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1067967.1067970","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1067967.1067970","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03707406v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03707406","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":"ACM Transactions on Mathematical Software, 2005, 31 (2), pp.228-238. &#x27E8;10.1145/1067967.1067970&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W90568776","https://openalex.org/W603380843","https://openalex.org/W1556040198","https://openalex.org/W1562714622","https://openalex.org/W1565837554","https://openalex.org/W1575701986","https://openalex.org/W1966287322","https://openalex.org/W1981883552","https://openalex.org/W1987507345","https://openalex.org/W2006567294","https://openalex.org/W2010315317","https://openalex.org/W2023567863","https://openalex.org/W2051512594","https://openalex.org/W2052087587","https://openalex.org/W2061771449","https://openalex.org/W2072430303","https://openalex.org/W2076926241","https://openalex.org/W2095222360","https://openalex.org/W2103719287","https://openalex.org/W2121555031","https://openalex.org/W2126841255","https://openalex.org/W2130674780","https://openalex.org/W2140153041","https://openalex.org/W2142399659","https://openalex.org/W2142670431","https://openalex.org/W2149381887","https://openalex.org/W2168203579","https://openalex.org/W2316540078","https://openalex.org/W2318666329","https://openalex.org/W3022909171","https://openalex.org/W4230252700","https://openalex.org/W4240893730","https://openalex.org/W4285019923","https://openalex.org/W4302564868","https://openalex.org/W6633532468"],"related_works":["https://openalex.org/W2002097440","https://openalex.org/W2000690703","https://openalex.org/W3152060313","https://openalex.org/W2484832770","https://openalex.org/W2103271089","https://openalex.org/W2028770117","https://openalex.org/W1995841910","https://openalex.org/W1990351032","https://openalex.org/W2127147063","https://openalex.org/W1596285621"],"abstract_inverted_index":{"In":[0],"this":[1],"article":[2],"we":[3],"describe":[4],"our":[5],"implementations":[6],"of":[7,33,78,88,99,111],"the":[8,31,39,49,54,57,60,76,79,91,100,108,112,116],"GMRES":[9,40],"algorithm":[10],"for":[11,22,53,90],"both":[12],"real":[13],"and":[14,17,26,37,59],"complex,":[15],"single":[16],"double":[18],"precision":[19],"arithmetics":[20],"suitable":[21],"serial,":[23],"shared":[24],"memory":[25,28,66],"distributed":[27,65],"computers.":[29],"For":[30,64],"sake":[32],"portability,":[34],"simplicity,":[35],"flexibility":[36],"efficiency":[38,89],"solvers":[41],"have":[42,71],"been":[43,72],"implemented":[44,73,117],"in":[45],"Fortran":[46],"77":[47],"using":[48],"reverse":[50],"communication":[51],"mechanism":[52],"matrix-vector":[55,113],"product,":[56],"preconditioning":[58],"dot":[61,80],"product":[62,81],"computations.":[63],"computation,":[67],"several":[68],"orthogonalization":[69],"procedures":[70],"to":[74],"reduce":[75],"cost":[77,110],"calculation,":[82],"which":[83],"is":[84,120],"a":[85,123],"well-known":[86],"bottleneck":[87],"Krylov":[92],"methods.":[93],"Either":[94],"implicit":[95],"or":[96],"explicit":[97],"calculation":[98],"residual":[101],"at":[102],"restart":[103],"are":[104],"possible":[105],"depending":[106],"on":[107,122],"actual":[109],"product.":[114],"Finally":[115],"stopping":[118],"criterion":[119],"based":[121],"normwise":[124],"backward":[125],"error.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
