{"id":"https://openalex.org/W4229454507","doi":"https://doi.org/10.1137/21m142931x","title":"Linearizable Eigenvector Nonlinearities","display_name":"Linearizable Eigenvector Nonlinearities","publication_year":2022,"publication_date":"2022-05-10","ids":{"openalex":"https://openalex.org/W4229454507","doi":"https://doi.org/10.1137/21m142931x"},"language":"en","primary_location":{"id":"doi:10.1137/21m142931x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m142931x","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":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/bitstream/20.500.12942/695420/2/main.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034702914","display_name":"Rob Claes","orcid":"https://orcid.org/0000-0001-6059-155X"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Rob Claes","raw_affiliation_strings":["Department of Computer Science, KU Leuven, Leuven, Belgium,"],"raw_orcid":"https://orcid.org/0000-0001-6059-155X","affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven, Leuven, Belgium,","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075035467","display_name":"Elias Jarlebring","orcid":"https://orcid.org/0000-0001-9443-8772"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Elias Jarlebring","raw_affiliation_strings":["Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, SeRC","Swedish"],"raw_orcid":"https://orcid.org/0000-0001-9443-8772","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, SeRC","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Swedish","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079388991","display_name":"Karl Meerbergen","orcid":"https://orcid.org/0000-0002-1508-0248"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Karl Meerbergen","raw_affiliation_strings":["Department of Computer Science, KU Leuven, Leuven, Belgium,"],"raw_orcid":"https://orcid.org/0000-0002-1508-0248","affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven, Leuven, Belgium,","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066031998","display_name":"Parikshit Upadhyaya","orcid":"https://orcid.org/0000-0002-2157-6418"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Parikshit Upadhyaya","raw_affiliation_strings":["Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, SeRC","Swedish"],"raw_orcid":"https://orcid.org/0000-0002-2157-6418","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, SeRC","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Swedish","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034702914"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.4525,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64647493,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"43","issue":"2","first_page":"764","last_page":"786"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9988999962806702,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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":0.8459205627441406},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7942520380020142},{"id":"https://openalex.org/keywords/inverse-iteration","display_name":"Inverse iteration","score":0.6689013838768005},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6643521189689636},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5889459252357483},{"id":"https://openalex.org/keywords/rayleigh-quotient-iteration","display_name":"Rayleigh quotient iteration","score":0.5718613862991333},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.5546978116035461},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4726009964942932},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4483637809753418},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44221821427345276},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4347218871116638},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4037911593914032},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.354134202003479},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.31587550044059753},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27752918004989624},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.22565051913261414},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20857661962509155}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8459205627441406},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7942520380020142},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.6689013838768005},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6643521189689636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5889459252357483},{"id":"https://openalex.org/C117586675","wikidata":"https://www.wikidata.org/wiki/Q7298489","display_name":"Rayleigh quotient iteration","level":4,"score":0.5718613862991333},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.5546978116035461},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4726009964942932},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4483637809753418},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44221821427345276},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4347218871116638},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4037911593914032},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.354134202003479},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31587550044059753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27752918004989624},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.22565051913261414},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20857661962509155},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":2,"locations":[{"id":"doi:10.1137/21m142931x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m142931x","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:lirias2repo.kuleuven.be:20.500.12942/695420","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/bitstream/20.500.12942/695420/2/main.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU 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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Siam Journal On Matrix Analysis And Applications, vol. 43 (2), (764-786)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/695420","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/bitstream/20.500.12942/695420/2/main.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU 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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Siam Journal On Matrix Analysis And Applications, vol. 43 (2), (764-786)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8805711408","display_name":null,"funder_award_id":"G0B7818N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320322681","display_name":"Onderzoeksraad, KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1852068959","https://openalex.org/W1964200011","https://openalex.org/W1983354332","https://openalex.org/W2013183108","https://openalex.org/W2013419029","https://openalex.org/W2017335040","https://openalex.org/W2024165284","https://openalex.org/W2057106305","https://openalex.org/W2057342157","https://openalex.org/W2065519604","https://openalex.org/W2071438440","https://openalex.org/W2073829819","https://openalex.org/W2088748973","https://openalex.org/W2091127828","https://openalex.org/W2115308285","https://openalex.org/W2117870622","https://openalex.org/W2141470953","https://openalex.org/W2143956837","https://openalex.org/W2157529542","https://openalex.org/W2169650761","https://openalex.org/W2198317436","https://openalex.org/W2341270922","https://openalex.org/W2889864884","https://openalex.org/W2896604562","https://openalex.org/W2898384941","https://openalex.org/W2962743802","https://openalex.org/W2963073920","https://openalex.org/W2964350126","https://openalex.org/W3013131092"],"related_works":["https://openalex.org/W3188219351","https://openalex.org/W4388185085","https://openalex.org/W2383442806","https://openalex.org/W2796073220","https://openalex.org/W4297437581","https://openalex.org/W1994155896","https://openalex.org/W22212747","https://openalex.org/W2890146710","https://openalex.org/W1549357804","https://openalex.org/W2472637427"],"abstract_inverted_index":{"We":[0,114,132],"present":[1],"a":[2,8,30,66,72,160,167,174],"method":[3],"to":[4,58,75,89,104,142],"linearize,":[5],"without":[6],"approximation,":[7],"specific":[9],"class":[10],"of":[11,32,35,54,61,65,109,111,123,149,166,176],"eigenvalue":[12,46,68],"problems":[13],"with":[14],"eigenvector":[15],"nonlinearities":[16,20],"(NEPv),":[17],"where":[18],"the":[19,36,51,55,59,87,99,107,112,121,124,137,156,164,177],"are":[21,27],"expressed":[22],"by":[23,29],"scalar":[24],"functions":[25,34],"that":[26,49,119,170],"defined":[28],"quotient":[31],"linear":[33,100],"eigenvector.":[37],"The":[38],"exact":[39,52],"linearization":[40],"relies":[41],"on":[42,173],"an":[43],"equivalent":[44],"multiparameter":[45],"problem":[47,69],"(MEP)":[48],"contains":[50],"solutions":[53,79,110],"NEPv.":[56,113],"Due":[57],"characterization":[60],"MEPs":[62],"in":[63,136],"terms":[64],"generalized":[67],"this":[70],"provides":[71],"direct":[73],"way":[74],"compute":[76],"all":[77],"NEPv":[78],"for":[80,95],"small":[81],"problems,":[82],"and":[83,128,145,159],"it":[84],"opens":[85],"up":[86],"possibility":[88],"develop":[90],"locally":[91],"convergent":[92],"iterative":[93],"methods":[94],"larger":[96],"problems.":[97],"Moreover,":[98],"formulation":[101],"allows":[102],"us":[103],"easily":[105],"determine":[106],"number":[108],"propose":[115],"two":[116,178],"numerical":[117,153],"schemes":[118],"exploit":[120],"structure":[122],"linearization:":[125],"inverse":[126,130],"iteration":[127],"residual":[129],"iteration.":[131],"show":[133],"how":[134],"symmetry":[135],"MEP":[138],"can":[139],"be":[140],"used":[141],"improve":[143],"reliability":[144],"reduce":[146],"computational":[147],"cost":[148],"both":[150],"methods.":[151,180],"Two":[152],"examples":[154],"verify":[155],"theoretical":[157],"results,":[158],"third":[161],"example":[162],"shows":[163],"potential":[165],"hybrid":[168],"scheme":[169],"is":[171],"based":[172],"combination":[175],"proposed":[179]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
