{"id":"https://openalex.org/W2052266798","doi":"https://doi.org/10.1080/00207169908804857","title":"Numerical methods for solving multiparameter eigenvalue problems","display_name":"Numerical methods for solving multiparameter eigenvalue problems","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2052266798","doi":"https://doi.org/10.1080/00207169908804857","mag":"2052266798"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804857","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804857","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5102023258","display_name":"Hua Dai","orcid":"https://orcid.org/0000-0003-2983-8627"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hua Dai","raw_affiliation_strings":["\n                   \n               Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People's Republic of China","Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"\n                   \n               Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People's Republic of China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People's Republic of China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102023258"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":0.45521319,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.61898279,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"72","issue":"3","first_page":"331","last_page":"347"},"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/T12037","display_name":"Algebraic and Geometric Analysis","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/T11191","display_name":"Mathematical functions and polynomials","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7263349890708923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6962897777557373},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5941872596740723},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.568005383014679},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.5122777819633484},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5097755789756775},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4625396728515625},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4337230920791626},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3579273223876953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23000341653823853}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7263349890708923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6962897777557373},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5941872596740723},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.568005383014679},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.5122777819633484},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5097755789756775},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4625396728515625},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4337230920791626},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3579273223876953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23000341653823853},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169908804857","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804857","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310537","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W617148876","https://openalex.org/W1510003436","https://openalex.org/W1536935890","https://openalex.org/W1573717114","https://openalex.org/W1968739206","https://openalex.org/W1984575885","https://openalex.org/W1996416313","https://openalex.org/W2002862998","https://openalex.org/W2008067113","https://openalex.org/W2013419029","https://openalex.org/W2016519641","https://openalex.org/W2022034805","https://openalex.org/W2022544098","https://openalex.org/W2024528718","https://openalex.org/W2027277486","https://openalex.org/W2028875955","https://openalex.org/W2029854885","https://openalex.org/W2032231305","https://openalex.org/W2037055076","https://openalex.org/W2047768782","https://openalex.org/W2062955373","https://openalex.org/W2081430409","https://openalex.org/W2085680806","https://openalex.org/W2090963365","https://openalex.org/W2129911318","https://openalex.org/W2171890171","https://openalex.org/W2313559663","https://openalex.org/W2320694971","https://openalex.org/W2577663557","https://openalex.org/W2588613786","https://openalex.org/W2798573187","https://openalex.org/W2798909945","https://openalex.org/W4210417322","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W46293795","https://openalex.org/W2350895707","https://openalex.org/W2014626854","https://openalex.org/W2963566796","https://openalex.org/W2383221329","https://openalex.org/W2364889976","https://openalex.org/W4285722889","https://openalex.org/W2040482695","https://openalex.org/W2776155623","https://openalex.org/W2369274133"],"abstract_inverted_index":{"Abstract":[0],"This":[1,79,95,112],"paper":[2],"is":[3,53],"concerned":[4],"with":[5],"the":[6,30,34,51,62,88,104,121],"numerical":[7,56],"solution":[8],"of":[9,19,37,50,66,93,109,126],"multiparameter":[10,20],"eigenvalue":[11,22,71],"problems":[12,23],"for":[13],"matrices":[14],"which":[15],"arise":[16],"in":[17,24,83,99,116],"discretization":[18],"Sturm-Liouville":[21],"ordinary":[25],"differential":[26],"equations.":[27],"Based":[28],"on":[29],"trace":[31],"theorem":[32,73],"and":[33,64],"differentiability":[35],"theory":[36],"QR":[38,74],"decomposition":[39],"two":[40],"new":[41],"algorithms":[42],"are":[43,58],"proposed.":[44],"The":[45],"locally":[46],"quadratic":[47],"convergence":[48],"analysis":[49],"methods":[52],"given.":[54],"Some":[55],"results":[57],"presented":[59],"to":[60],"illustrate":[61],"performance":[63],"application":[65],"our":[67],"methods.":[68],"Keywords:":[69],"Multiparameter":[70],"problemstrace":[72],"decompositionNewton's":[75],"methodC.R.":[76],"Categories:":[77],"G1.3G1.7":[78],"work":[80,96,113],"was":[81,97,114],"supported":[82,98,115],"part":[84,100,117],"by":[85,101,118],"grant":[86,102,119],"from":[87,103,120],"National":[89,105,122],"Natural":[90,106,123],"Science":[91,107,124],"Foundation":[92,108,125],"China.":[94,110,127],"Notes":[111]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
