{"id":"https://openalex.org/W2073865064","doi":"https://doi.org/10.1137/0915006","title":"A Family of Quasi-Minimal Residual Methods for Nonsymmetric Linear Systems","display_name":"A Family of Quasi-Minimal Residual Methods for Nonsymmetric Linear Systems","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W2073865064","doi":"https://doi.org/10.1137/0915006","mag":"2073865064"},"language":"en","primary_location":{"id":"doi:10.1137/0915006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915006","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5104225579","display_name":"Charles Tong","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Charles H. Tong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5104225579"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.13,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.86397713,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"1","first_page":"89","last_page":"105"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9975000023841858,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9969000220298767,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.8865379691123962},{"id":"https://openalex.org/keywords/biconjugate-gradient-stabilized-method","display_name":"Biconjugate gradient stabilized method","score":0.8201700448989868},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7130604386329651},{"id":"https://openalex.org/keywords/biconjugate-gradient-method","display_name":"Biconjugate gradient method","score":0.677126944065094},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6166326403617859},{"id":"https://openalex.org/keywords/transpose","display_name":"Transpose","score":0.5801808834075928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5391794443130493},{"id":"https://openalex.org/keywords/method-of-mean-weighted-residuals","display_name":"Method of mean weighted residuals","score":0.4129132032394409},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4063132107257843},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.32353246212005615},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.23938044905662537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21303609013557434},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1348048448562622}],"concepts":[{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.8865379691123962},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.8201700448989868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7130604386329651},{"id":"https://openalex.org/C89408827","wikidata":"https://www.wikidata.org/wiki/Q855169","display_name":"Biconjugate gradient method","level":5,"score":0.677126944065094},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6166326403617859},{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.5801808834075928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5391794443130493},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.4129132032394409},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4063132107257843},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.32353246212005615},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.23938044905662537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21303609013557434},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1348048448562622},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0915006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915006","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1571187512","https://openalex.org/W2021810545","https://openalex.org/W2026639176","https://openalex.org/W2044557804","https://openalex.org/W2049036377","https://openalex.org/W2049644675","https://openalex.org/W2085259167","https://openalex.org/W2117366131","https://openalex.org/W2140153041","https://openalex.org/W2147542748","https://openalex.org/W2155216327","https://openalex.org/W2316564661"],"related_works":["https://openalex.org/W2069713958","https://openalex.org/W2109622333","https://openalex.org/W2093107138","https://openalex.org/W2950173424","https://openalex.org/W4299356399","https://openalex.org/W2500063501","https://openalex.org/W1994435314","https://openalex.org/W2273268247","https://openalex.org/W2058903283","https://openalex.org/W1985372460"],"abstract_inverted_index":{"The":[0,141],"quasi-minimal":[1,62,81,152,159,177,181],"residual":[2,63,82,98,153,160,178,182],"(QMR)":[3],"algorithm":[4],"by":[5,46],"Freund,":[6],"Gutknecht,":[7],"and":[8,95,179],"Nachtigal":[9],"[Research":[10],"Institute":[11],"forAdvanced":[12],"Computer":[13],"Science":[14],"Tech.":[15],"Report":[16],"91.09,":[17],"NASA":[18],"Ames":[19],"Research":[20],"Center,":[21],"Moffett":[22],"Field,":[23],"CA;":[24],"Numer.":[25],"Math.,":[26],"60":[27],"(1991),":[28],"pp.":[29],"315\u2013339],":[30],"in":[31,102,185],"addition":[32],"to":[33,36,68,113,147],"its":[34],"ability":[35],"avoid":[37],"breakdowns,":[38],"also":[39,145],"improves":[40],"the":[41,47,53,69,73,91,105,123,163,176],"irregular":[42],"convergence":[43,133],"behavior":[44,134],"encountered":[45],"biconjugate":[48],"gradient":[49],"(BiCG)":[50],"method":[51,94,99,168],"through":[52],"incorporation":[54],"of":[55,72,80,162],"quasi":[56],"minimization.":[57],"This":[58],"paper":[59],"studies":[60],"this":[61,186],"approach":[64],"applied,":[65],"for":[66],"simplicity,":[67],"nonlook-ahead":[70],"version":[71],"QMR":[74,93,125],"method.":[75,154],"In":[76,155],"particular,":[77,156],"a":[78,96,115,148,157],"family":[79],"methods":[83],"is":[84],"defined":[85],"where":[86],"on":[87],"both":[88],"ends":[89],"lie":[90],"original":[92,124],"minimal":[97],"while":[100],"lying":[101],"between":[103],"are":[104,111,169,173],"variants":[106,110,161,183],"derived":[107,184],"here.":[108],"These":[109],"shown":[112],"consume":[114],"little":[116],"more":[117],"computational":[118],"work":[119],"per":[120],"iterations":[121],"than":[122],"method,":[126],"but":[127],"generally":[128],"give":[129],"an":[130],"even":[131],"better":[132],"as":[135,137],"well":[136],"lower":[138],"iteration":[139],"counts.":[140],"same":[142],"idea":[143],"was":[144],"applied":[146],"recently":[149],"proposed":[150],"transpose-free":[151,180],"few":[158],"Van":[164],"der":[165],"Vorst":[166],"BiCGSTAB":[167],"derived.":[170],"Numerical":[171],"results":[172],"presented":[174],"comparing":[175],"paper.":[187]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
