{"id":"https://openalex.org/W2331234901","doi":"https://doi.org/10.1137/14099231x","title":"An Algorithm for the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils by Minimal Perturbation Approach","display_name":"An Algorithm for the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils by Minimal Perturbation Approach","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2331234901","doi":"https://doi.org/10.1137/14099231x","mag":"2331234901"},"language":"en","primary_location":{"id":"doi:10.1137/14099231x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14099231x","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/A5101060441","display_name":"Shinji Ito","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shinji Ito","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032957138","display_name":"Kazuo Murota","orcid":"https://orcid.org/0000-0003-1518-9152"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kazuo Murota","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5232,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89901897,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"37","issue":"1","first_page":"409","last_page":"419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7990602254867554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7687689661979675},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.710832953453064},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.6889092326164246},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6268690824508667},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6207455396652222},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5970162749290466},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3761376142501831},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35442304611206055}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7990602254867554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7687689661979675},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.710832953453064},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.6889092326164246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6268690824508667},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6207455396652222},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5970162749290466},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3761376142501831},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35442304611206055},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/14099231x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14099231x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1965683017","https://openalex.org/W1993068751","https://openalex.org/W2008229822","https://openalex.org/W2015320521","https://openalex.org/W2016651309","https://openalex.org/W2032604276","https://openalex.org/W2056509440","https://openalex.org/W2064431362","https://openalex.org/W2064980127","https://openalex.org/W2074702686","https://openalex.org/W2078084493","https://openalex.org/W2091129013","https://openalex.org/W2102062010","https://openalex.org/W2128217535","https://openalex.org/W2135631911","https://openalex.org/W4205696294"],"related_works":["https://openalex.org/W2047937394","https://openalex.org/W2806574890","https://openalex.org/W2330447052","https://openalex.org/W4387938021","https://openalex.org/W2390920986","https://openalex.org/W2734992995","https://openalex.org/W3138597860","https://openalex.org/W1992815519","https://openalex.org/W4289785680","https://openalex.org/W2030428360"],"abstract_inverted_index":{"We":[0],"deal":[1],"with":[2,69,153],"the":[3,64,92,96,100,112,117,147,151,162,191],"generalized":[4],"eigenvalue":[5],"problem":[6,43,152,166],"$A{\\bm":[7],"x}":[8],"=":[9],"\\lambda":[10,21],"B":[11,22,28],"{\\bm":[12],"x}$":[13],"for":[14,91,126,146],"nonsquare":[15],"matrix":[16],"pencils":[17],"$":[18,25],"A":[19,26,37],"-":[20],"$,":[23],"where":[24],",":[27],"\\in":[29],"\\mathbb{C}^{m":[30],"\\times":[31],"n}$":[32],"and":[33,170,178],"$m":[34],">":[35],"n$.":[36],"major":[38],"difficulty":[39],"inherent":[40],"in":[41,63],"this":[42,70,139],"is":[44,141,159,175,187,194],"that":[45,89,99,116,130,190],"perturbation":[46,94,114],"to":[47,52,54,61,95,142],"inputs":[48],"may":[49],"cause":[50],"eigenvalues":[51,58],"fail":[53],"exist":[55,62],"even":[56],"if":[57],"are":[59],"known":[60],"noiseless":[65],"case.":[66],"To":[67],"cope":[68],"situation,":[71],"Boutry":[72,105,182,201],"et":[73,106,183,202],"al.":[74,107],"[SIAM":[75],"J.":[76],"Matrix":[77],"Anal.":[78],"Appl.,":[79],"27":[80],"(2005),":[81],"pp.":[82],"582--601]":[83],"have":[84],"proposed":[85,157,192],"a":[86,127],"novel":[87],"approach":[88],"searches":[90],"minimal":[93,113],"pencil":[97,102,119],"such":[98,115],"perturbed":[101,118],"has":[103,120],"eigenpairs.":[104,155],"first":[108],"aimed":[109],"at":[110,132],"finding":[111],"$n$":[121,154],"eigenpairs,":[122],"but":[123],"they":[124],"settled":[125],"simplified":[128],"version":[129,149],"guarantees":[131],"least":[133,164],"one":[134],"eigenpair.":[135],"The":[136,156,173],"aim":[137],"of":[138,150],"paper":[140],"present":[143],"an":[144],"algorithm":[145,158,174,193],"original":[148],"based":[160],"on":[161],"total":[163],"squares":[165],"introduced":[167],"by":[168],"Golub":[169],"Van":[171],"Loan.":[172],"much":[176],"simpler":[177],"runs":[179],"faster":[180],"than":[181,200],"al.'s":[184,203],"algorithm.":[185,204],"It":[186],"confirmed":[188],"numerically":[189],"more":[195],"robust":[196],"against":[197],"data":[198],"noise":[199]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
