{"id":"https://openalex.org/W2258717409","doi":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<275::aid-nla131>3.0.co;2-b","title":"A new adaptive GMRES algorithm for achieving high accuracy","display_name":"A new adaptive GMRES algorithm for achieving high accuracy","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2258717409","doi":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<275::aid-nla131>3.0.co;2-b","mag":"2258717409"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199807/08)5:4<275::aid-nla131>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<275::aid-nla131>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/433394","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113739735","display_name":"Maria Sosonkina","orcid":null},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Maria Sosonkina","raw_affiliation_strings":["Departments of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0106, USA"],"affiliations":[{"raw_affiliation_string":"Departments of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0106, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068161656","display_name":"Layne T. Watson","orcid":"https://orcid.org/0000-0003-2009-107X"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Layne T. Watson","raw_affiliation_strings":["Departments of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0106, USA"],"affiliations":[{"raw_affiliation_string":"Departments of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0106, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051452494","display_name":"Rakesh K. Kapania","orcid":"https://orcid.org/0000-0001-7294-4703"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rakesh K. Kapania","raw_affiliation_strings":["Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0203, USA"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0203, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049591038","display_name":"Homer F. Walker","orcid":null},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Homer F. Walker","raw_affiliation_strings":["Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609-2280, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609-2280, USA","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5113739735"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.9682,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.76953077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"5","issue":"4","first_page":"275","last_page":"297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987999796867371,"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":0.9984999895095825,"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":0.9750521183013916},{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.9039584398269653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5732244253158569},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5519480109214783},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4682985842227936},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36983370780944824},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3556968569755554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1141110360622406}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.9750521183013916},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.9039584398269653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5732244253158569},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5519480109214783},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4682985842227936},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36983370780944824},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3556968569755554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1141110360622406}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199807/08)5:4<275::aid-nla131>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199807/08)5:4<275::aid-nla131>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.3846","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.3846","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://phase.etl.go.jp/mirrors/mgnet/mgnet/Conferences/CMCIM96/sosonkina-kapania-walker-watson.ps.gz","raw_type":"text"},{"id":"pmh:oai:osti.gov:433394","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/433394","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:vtcstechreports.OAI2:448","is_oa":false,"landing_page_url":"http://eprints.cs.vt.edu/archive/00000448/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400253","display_name":"Computer Science Technical Reports (Virginia Tech)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I859038795","host_organization_name":"Virginia Tech","host_organization_lineage":["https://openalex.org/I859038795"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Departmental Technical Report"},{"id":"pmh:oai:vtechworks.lib.vt.edu:10919/19899","is_oa":false,"landing_page_url":"http://hdl.handle.net/10919/19899","pdf_url":null,"source":{"id":"https://openalex.org/S4306400248","display_name":"VTechWorks (Virginia Tech)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I859038795","host_organization_name":"Virginia Tech","host_organization_lineage":["https://openalex.org/I859038795"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:osti.gov:433394","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/433394","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1521548175","https://openalex.org/W1965366611","https://openalex.org/W1971662204","https://openalex.org/W1976222070","https://openalex.org/W1989871666","https://openalex.org/W1995663965","https://openalex.org/W2000690703","https://openalex.org/W2020767300","https://openalex.org/W2021694321","https://openalex.org/W2027212082","https://openalex.org/W2040066775","https://openalex.org/W2041519450","https://openalex.org/W2041876368","https://openalex.org/W2057691949","https://openalex.org/W2067941796","https://openalex.org/W2075904090","https://openalex.org/W2083232784","https://openalex.org/W2085259167","https://openalex.org/W2113830538","https://openalex.org/W2121920162","https://openalex.org/W2127925969","https://openalex.org/W2140153041","https://openalex.org/W2166885897","https://openalex.org/W2786892008","https://openalex.org/W6631226450"],"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":{"GMRES(k)":[0,49,73,154,164],"is":[1,11,68,128,149,183],"widely":[2],"used":[3,34],"for":[4,18,64,105,185],"solving":[5],"non-symmetric":[6],"linear":[7,125],"systems.":[8],"However,":[9],"it":[10,15],"inadequate":[12],"either":[13],"when":[14,26],"converges":[16],"only":[17],"k":[19,55],"close":[20],"to":[21,146],"the":[22,30,36,42,52,60,65,124,133,142,152,156,166,170,176],"problem":[23,67],"size":[24],"or":[25],"numerical":[27],"error":[28],"in":[29,35,123,137],"modified":[31,134,171],"Gram\u2013Schmidt":[32,135,172],"process":[33,136,173],"GMRES":[37,61,144],"orthogonalization":[38,157,167],"phase":[39],"dramatically":[40],"affects":[41],"algorithm":[43],"performance.":[44],"An":[45],"adaptive":[46,72,153],"version":[47],"of":[48,179],"which":[50],"tunes":[51],"restart":[53],"value":[54],"based":[56],"on":[57,84],"criteria":[58],"estimating":[59],"convergence":[62],"rate":[63],"given":[66],"proposed":[69],"here.":[70],"This":[71],"procedure":[74],"outperforms":[75],"standard":[76],"GMRES(k),":[77],"several":[78],"other":[79],"GMRES-like":[80],"methods,":[81],"and":[82,92,115,175],"QMR":[83],"actual":[85],"large":[86],"scale":[87],"sparse":[88],"structural":[89],"mechanics":[90,112],"postbuckling":[91,113],"analog":[93,116],"circuit":[94,117],"simulation":[95],"problems.":[96],"There":[97],"are":[98],"some":[99],"applications,":[100],"such":[101],"as":[102],"homotopy":[103],"methods":[104],"high":[106,121],"Reynolds":[107],"number":[108],"viscous":[109],"flows,":[110],"solid":[111],"analysis,":[114],"simulation,":[118],"where":[119],"very":[120],"accuracy":[122],"system":[126],"solutions":[127],"essential.":[129],"In":[130],"this":[131],"context,":[132],"GMRES,":[138],"can":[139],"fail":[140],"causing":[141],"entire":[143],"iteration":[145],"fail.":[147],"It":[148],"shown":[150],"that":[151],"with":[155,165],"performed":[158,168],"by":[159,169],"Householder":[160,181],"transformations":[161,182],"succeeds":[162],"whenever":[163],"fails,":[174],"extra":[177],"cost":[178],"computing":[180],"justified":[184],"these":[186],"applications.":[187],"\u00a9":[188],"1998":[189],"John":[190],"Wiley":[191],"&":[192],"Sons,":[193],"Ltd.":[194]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
