{"id":"https://openalex.org/W2099514750","doi":"https://doi.org/10.1137/s106482759935174x","title":"Locking and Restarting Quadratic Eigenvalue Solvers","display_name":"Locking and Restarting Quadratic Eigenvalue Solvers","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2099514750","doi":"https://doi.org/10.1137/s106482759935174x","mag":"2099514750"},"language":"en","primary_location":{"id":"doi:10.1137/s106482759935174x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759935174x","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2078.1/42835","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079388991","display_name":"Karl Meerbergen","orcid":"https://orcid.org/0000-0002-1508-0248"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Karl Meerbergen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079388991"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4635,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.9317797,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"5","first_page":"1814","last_page":"1839"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.7680668830871582},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7006028294563293},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6727175116539001},{"id":"https://openalex.org/keywords/schur-decomposition","display_name":"Schur decomposition","score":0.629790186882019},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6041774749755859},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5719942450523376},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.565844714641571},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5274391770362854},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.5229276418685913},{"id":"https://openalex.org/keywords/arnoldi-iteration","display_name":"Arnoldi iteration","score":0.461825430393219},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.4568804204463959},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.4329395294189453},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.4045308828353882},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.38497471809387207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33003729581832886},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19033601880073547},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11230355501174927},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07055920362472534}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7680668830871582},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7006028294563293},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6727175116539001},{"id":"https://openalex.org/C99383703","wikidata":"https://www.wikidata.org/wiki/Q1064218","display_name":"Schur decomposition","level":4,"score":0.629790186882019},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6041774749755859},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5719942450523376},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.565844714641571},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5274391770362854},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5229276418685913},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.461825430393219},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.4568804204463959},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.4329395294189453},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.4045308828353882},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.38497471809387207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33003729581832886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19033601880073547},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11230355501174927},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07055920362472534},{"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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s106482759935174x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759935174x","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"},{"id":"pmh:hdl:10068/653903","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/653903","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:cds.cern.ch:381246","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/381246","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:dial.uclouvain.be:boreal:42835","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/42835","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"SIAM Journal on Scientific Computing, Vol. 22, no. 5, p. 1814-1839 (2001)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:epubs.cclrc.ac.uk:work/29616","is_oa":false,"landing_page_url":"http://purl.org/net/epubs/work/29616","pdf_url":null,"source":{"id":"https://openalex.org/S4306400334","display_name":"Science and Technology Facilities Council","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:dial.uclouvain.be:boreal:42835","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/42835","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"SIAM Journal on Scientific Computing, Vol. 22, no. 5, p. 1814-1839 (2001)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1563653928","https://openalex.org/W1979655951","https://openalex.org/W1980431326","https://openalex.org/W1984720662","https://openalex.org/W1988107764","https://openalex.org/W1988464212","https://openalex.org/W1988662661","https://openalex.org/W1990238127","https://openalex.org/W1993987675","https://openalex.org/W2022393550","https://openalex.org/W2027389940","https://openalex.org/W2030787165","https://openalex.org/W2032918887","https://openalex.org/W2033307991","https://openalex.org/W2069262775","https://openalex.org/W2082712935","https://openalex.org/W2086160340","https://openalex.org/W2086678890","https://openalex.org/W2092407721","https://openalex.org/W2095222360","https://openalex.org/W2097390250","https://openalex.org/W2106869373","https://openalex.org/W2116732229","https://openalex.org/W2140153041","https://openalex.org/W2141470953","https://openalex.org/W2160685034","https://openalex.org/W2163336887","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2015942935","https://openalex.org/W3134028852","https://openalex.org/W2037894849","https://openalex.org/W2804908571","https://openalex.org/W2169765983","https://openalex.org/W2034236710","https://openalex.org/W2058557317","https://openalex.org/W2148733093","https://openalex.org/W1986035204","https://openalex.org/W2151478420"],"abstract_inverted_index":{"This":[0,134],"paper":[1,135],"studies":[2],"the":[3,10,29,35,66,72,86,97,100,107,119,123,147,154,157,160,172,176,195,205],"solution":[4],"of":[5,53,65,92,99,106,156,175],"quadratic":[6,11,108,111,120,143,158,180,188],"eigenvalue":[7,42,144],"problems":[8,145],"by":[9,74,163],"residual":[12,112,181,189],"iteration":[13,113,182,190],"method.":[14,208],"The":[15,90,110],"focus":[16],"is":[17,28,43,46,95,103,126],"on":[18,171],"applications":[19],"arising":[20],"from":[21],"finite-element":[22],"simulations":[23],"in":[24,179],"acoustics.":[25],"One":[26],"approach":[27,94],"shift-and-invert":[30,206],"Arnoldi":[31,207],"method":[32,73],"applied":[33],"to":[34,48,61,152],"linearized":[36,101,148,161,177],"problem.":[37,109,121,149],"When":[38],"more":[39],"than":[40],"one":[41,69],"wanted,":[44],"it":[45],"advisable":[47],"use":[49,85],"locking":[50,82,131,166],"or":[51],"deflation":[52],"converged":[54],"eigenvectors":[55,77],"(or":[56,78],"Schur":[57,79,88,124,173,197],"vectors).":[58,80],"In":[59],"order":[60],"avoid":[62],"unlimited":[63],"growth":[64],"subspace":[67],"dimension,":[68],"can":[70],"restart":[71],"purging":[75],"unwanted":[76],"Both":[81],"and":[83,114,132,146,159,167,183,191],"restarting":[84,168],"partial":[87],"form.":[89,198],"disadvantage":[91],"this":[93],"that":[96,105],"dimension":[98],"problem":[102,178],"twice":[104],"Jacobi--Davidson":[115,192],"methods":[116,140],"directly":[117],"solve":[118],"Unfortunately,":[122],"form":[125,174],"not":[127],"defined,":[128],"nor":[129],"are":[130],"restarting.":[133],"shows":[136],"a":[137,165,202],"link":[138],"between":[139],"for":[141,193],"solving":[142],"It":[150,199],"aims":[151],"combine":[153],"benefits":[155],"approaches":[162],"employing":[164],"scheme":[169],"based":[170],"Jacobi--Davidson.":[184],"Numerical":[185],"experiments":[186],"illustrate":[187],"computing":[194],"linear":[196],"also":[200],"makes":[201],"comparison":[203],"with":[204]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
