{"id":"https://openalex.org/W2750780521","doi":"https://doi.org/10.1137/17m1144167","title":"Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems","display_name":"Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2750780521","doi":"https://doi.org/10.1137/17m1144167","mag":"2750780521"},"language":"en","primary_location":{"id":"doi:10.1137/17m1144167","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1144167","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":"https://lirias.kuleuven.be/handle/123456789/629837","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037538261","display_name":"Pieter Lietaert","orcid":"https://orcid.org/0000-0002-4085-1067"},"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":"Pieter Lietaert","raw_affiliation_strings":["Department of Computer Science, KU Leuven, University of Leuven, 3001 Heverlee, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven, University of Leuven, 3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"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, University of Leuven, 3001 Heverlee, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven, University of Leuven, 3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059791596","display_name":"Fran\u00e7oise Tisseur","orcid":"https://orcid.org/0000-0002-1011-2570"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fran\u00e7oise Tisseur","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037538261"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":2.0193,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.87857569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"5","first_page":"A2801","last_page":"A2829"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9968000054359436,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9959999918937683,"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":0.8375489711761475},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7089173793792725},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5575305223464966},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5322777032852173},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5222371816635132},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5040001273155212},{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.4711158275604248},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.4460938572883606},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.4385259449481964},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.41300705075263977},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35871827602386475},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3451770544052124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2861614525318146},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.27507174015045166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1446242332458496}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8375489711761475},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7089173793792725},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5575305223464966},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5322777032852173},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5222371816635132},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5040001273155212},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.4711158275604248},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.4460938572883606},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.4385259449481964},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.41300705075263977},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35871827602386475},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3451770544052124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2861614525318146},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.27507174015045166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1446242332458496},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1144167","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1144167","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:oai:lirias2repo.kuleuven.be:123456789/629837","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/629837","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Siam Journal On Scientific Computing, vol. 40 (5), (A2801-A2829)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.atira.dk:publications/4175c675-6374-41db-aa3d-e14fde2f74ac","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/4175c675-6374-41db-aa3d-e14fde2f74ac","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"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:lirias2repo.kuleuven.be:123456789/629837","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/629837","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Siam Journal On Scientific Computing, vol. 40 (5), (A2801-A2829)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G210194500","display_name":null,"funder_award_id":"IAP V11/19","funder_id":"https://openalex.org/F4320321454","funder_display_name":"Belgian Federal Science Policy Office"},{"id":"https://openalex.org/G2449384599","display_name":null,"funder_award_id":"EP/I005293/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7434063081","display_name":null,"funder_award_id":"OT/14/074","funder_id":"https://openalex.org/F4320322681","funder_display_name":"Onderzoeksraad, KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320321454","display_name":"Belgian Federal Science Policy Office","ror":"https://ror.org/01fapfv42"},{"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},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W51717795","https://openalex.org/W77858319","https://openalex.org/W1563813142","https://openalex.org/W1783139709","https://openalex.org/W1881137186","https://openalex.org/W1976429547","https://openalex.org/W1977424948","https://openalex.org/W1982342918","https://openalex.org/W1982604350","https://openalex.org/W2022226008","https://openalex.org/W2023509403","https://openalex.org/W2052604766","https://openalex.org/W2053530764","https://openalex.org/W2075664454","https://openalex.org/W2078578549","https://openalex.org/W2086742230","https://openalex.org/W2092407721","https://openalex.org/W2095222360","https://openalex.org/W2106034969","https://openalex.org/W2157355447","https://openalex.org/W2157859159","https://openalex.org/W2159901087","https://openalex.org/W2163336887","https://openalex.org/W2166325531","https://openalex.org/W2279865562","https://openalex.org/W2301036970","https://openalex.org/W2395882587","https://openalex.org/W2471719360","https://openalex.org/W2598027716","https://openalex.org/W2605949786"],"related_works":["https://openalex.org/W2592657418","https://openalex.org/W2060019775","https://openalex.org/W2083756075","https://openalex.org/W1579155259","https://openalex.org/W1990351032","https://openalex.org/W2072303989","https://openalex.org/W30053609","https://openalex.org/W4298211684","https://openalex.org/W2619829621","https://openalex.org/W2035969141"],"abstract_inverted_index":{"We":[0,219],"describe":[1],"a":[2,35,48,63,121,169,213,232],"generalization":[3,113],"of":[4,28,37,57,85,109,114,123,137,162,168,175,190],"the":[5,42,54,58,73,107,115,132,135,141,166,173,188,206],"compact":[6,68,183,192],"rational":[7,14,26,45,193],"Krylov":[8,65,180,194],"(CORK)":[9],"methods":[10,39,195],"for":[11,106,172,196,231],"polynomial":[12,24,43],"and":[13,70,76,93,140,148,178,185],"eigenvalue":[15,31,50,198],"problems":[16],"that":[17,40,79,127,222],"usually,":[18],"but":[19,98],"not":[20,100],"necessarily,":[21],"come":[22],"from":[23],"or":[25,44],"approximations":[27],"genuinely":[29],"nonlinear":[30,197],"problems.":[32,199],"CORK":[33,90,116,133,138,227],"is":[34,99,118,210],"family":[36],"one-sided":[38],"reformulates":[41],"eigenproblem":[46],"as":[47,129],"generalized":[49],"problem.":[51],"By":[52],"exploiting":[53],"Kronecker":[55,124],"structure":[56],"associated":[59,82],"pencil,":[60],"it":[61],"constructs":[62],"right":[64,96],"subspace":[66],"in":[67,102,182],"form":[69,105],"thereby":[71],"avoids":[72],"high":[74,86],"memory":[75],"orthogonalization":[77],"costs":[78],"are":[80,202],"usually":[81],"with":[83],"linearizations":[84,144],"degree":[87],"matrix":[88],"polynomials.":[89],"approximates":[91],"eigenvalues":[92],"their":[94],"corresponding":[95],"eigenvectors":[97],"suitable":[101],"its":[103],"current":[104],"computation":[108,174],"left":[110],"eigenvectors.":[111],"Our":[112],"method":[117],"based":[119],"on":[120],"class":[122,161],"structured":[125,143,163],"pencils":[126,164],"include":[128],"special":[130],"cases":[131],"pencils,":[134,139],"transposes":[136],"symmetrically":[142],"by":[145,212],"Robol,":[146],"Vandebril,":[147],"Van":[149],"Dooren":[150],"[SIAM":[151],"J.":[152],"Matrix":[153],"Anal.":[154],"Appl.,":[155],"38":[156],"(2017),":[157],"pp.":[158],"188--216].":[159],"This":[160],"facilitates":[165],"development":[167,189],"general":[170],"framework":[171],"both":[176],"right-":[177],"left-sided":[179],"subspaces":[181],"form,":[184],"hence":[186],"allows":[187],"two-sided":[191],"The":[200],"latter":[201],"particularly":[203],"efficient":[204],"when":[205],"standard":[207],"inner":[208],"product":[209],"replaced":[211],"cheaper":[214],"to":[215,226],"compute":[216],"quasi-inner":[217,234],"product.":[218,235],"show":[220],"experimentally":[221],"convergence":[223],"results":[224],"similar":[225],"can":[228],"be":[229],"obtained":[230],"certain":[233]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
