{"id":"https://openalex.org/W1968743256","doi":"https://doi.org/10.1137/130946009","title":"Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems","display_name":"Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1968743256","doi":"https://doi.org/10.1137/130946009","mag":"1968743256"},"language":"en","primary_location":{"id":"doi:10.1137/130946009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130946009","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034814306","display_name":"Keiichi Morikuni","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Keiichi Morikuni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072176609","display_name":"Ken Hayami","orcid":"https://orcid.org/0000-0001-9640-586X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ken Hayami","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.235,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.94403583,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"36","issue":"1","first_page":"225","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.9984999895095825,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9972000122070312,"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/mathematics","display_name":"Mathematics","score":0.891811728477478},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.7318809032440186},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6973381042480469},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6269210577011108},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6161879897117615},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5879200100898743},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4811362326145172},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.48065268993377686},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.45291563868522644},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4495684504508972},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32770299911499023},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2655196785926819},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24034357070922852},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1967402696609497},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06782853603363037}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.891811728477478},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.7318809032440186},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6973381042480469},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6269210577011108},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6161879897117615},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5879200100898743},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4811362326145172},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.48065268993377686},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.45291563868522644},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4495684504508972},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32770299911499023},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2655196785926819},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24034357070922852},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1967402696609497},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06782853603363037},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130946009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130946009","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:asep.lib.cas.cz:CavUnEpca/0438625","is_oa":false,"landing_page_url":"http://hdl.handle.net/11104/0242032","pdf_url":null,"source":{"id":"https://openalex.org/S7407055266","display_name":"ASEP","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1391371670","display_name":"Iterative Methods for Least Squares Problems and their Application to Inverse Problems","funder_award_id":"24560082","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2713586455","display_name":"The fast solution of least squares problems and its applications.","funder_award_id":"15K04768","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1971116595","https://openalex.org/W1977061454","https://openalex.org/W1983886273","https://openalex.org/W1986513558","https://openalex.org/W1998209214","https://openalex.org/W2000165536","https://openalex.org/W2018850201","https://openalex.org/W2024978582","https://openalex.org/W2041257655","https://openalex.org/W2044262951","https://openalex.org/W2054967989","https://openalex.org/W2064986275","https://openalex.org/W2067941796","https://openalex.org/W2071439344","https://openalex.org/W2081178476","https://openalex.org/W2083229815","https://openalex.org/W2084864145","https://openalex.org/W2097897435","https://openalex.org/W2128038070","https://openalex.org/W2140153041","https://openalex.org/W2155216327","https://openalex.org/W2313084557","https://openalex.org/W2316564661","https://openalex.org/W4254655041"],"related_works":["https://openalex.org/W2379775470","https://openalex.org/W2467000395","https://openalex.org/W2757608559","https://openalex.org/W2016713983","https://openalex.org/W1993237915","https://openalex.org/W3134028852","https://openalex.org/W2415566216","https://openalex.org/W2109728563","https://openalex.org/W2168284883","https://openalex.org/W2316400766"],"abstract_inverted_index":{"We":[0,30,71],"develop":[1],"a":[2,95],"general":[3],"convergence":[4,96],"theory":[5,48],"for":[6,16,35,89,98,119],"the":[7,42,68,74,77,82,86,90,99,107],"generalized":[8],"minimal":[9],"residual":[10],"method":[11],"preconditioned":[12,78],"by":[13,26,81],"inner":[14,22,38,91],"iterations":[15,23,39,92],"solving":[17],"least":[18],"squares":[19],"problems.":[20,122],"The":[21,47],"are":[24,110],"performed":[25],"stationary":[27],"iterative":[28],"methods.":[29,46,101],"also":[31,72],"present":[32],"theoretical":[33],"justifications":[34],"using":[36],"specific":[37],"such":[40],"as":[41],"Jacobi":[43],"and":[44,54,93,113],"SOR-type":[45],"improves":[49],"previous":[50,117],"work":[51],"[K.":[52],"Morikuni":[53],"K.":[55],"Hayami,":[56],"SIAM":[57],"J.":[58],"Matrix":[59],"Anal.":[60],"Appl.,":[61],"34":[62],"(2013),":[63],"pp.":[64],"1--22],":[65],"particularly":[66],"in":[67],"rank-deficient":[69,121],"case.":[70],"characterize":[73],"spectrum":[75],"of":[76,85],"coefficient":[79],"matrix":[80,88],"spectral":[83],"radius":[84],"iteration":[87],"give":[94],"bound":[97],"proposed":[100,108],"Finally,":[102],"numerical":[103],"experiments":[104],"show":[105],"that":[106],"methods":[109,118],"more":[111],"robust":[112],"efficient":[114],"compared":[115],"to":[116],"some":[120]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
