{"id":"https://openalex.org/W2045738033","doi":"https://doi.org/10.1137/140953150","title":"Fast Enclosure for All Eigenvalues and Invariant Subspaces in Generalized Eigenvalue Problems","display_name":"Fast Enclosure for All Eigenvalues and Invariant Subspaces in Generalized Eigenvalue Problems","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2045738033","doi":"https://doi.org/10.1137/140953150","mag":"2045738033"},"language":"en","primary_location":{"id":"doi:10.1137/140953150","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140953150","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/A5081777444","display_name":"Shinya Miyajima","orcid":"https://orcid.org/0000-0002-1642-0961"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shinya Miyajima","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081777444"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8486,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.90733631,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"35","issue":"3","first_page":"1205","last_page":"1225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.989300012588501,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9835000038146973,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.9009445905685425},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8359413146972656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7948271036148071},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6744817495346069},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.5931354761123657},{"id":"https://openalex.org/keywords/eigenvalue-perturbation","display_name":"Eigenvalue perturbation","score":0.5918434858322144},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.5832172632217407},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4028072953224182},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3852721154689789},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36157411336898804},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3468136787414551},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34210410714149475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.323297917842865},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06490683555603027}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.9009445905685425},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8359413146972656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7948271036148071},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6744817495346069},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.5931354761123657},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.5918434858322144},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.5832172632217407},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4028072953224182},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3852721154689789},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36157411336898804},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3468136787414551},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34210410714149475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.323297917842865},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06490683555603027},{"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":1,"locations":[{"id":"doi:10.1137/140953150","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140953150","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":10,"referenced_works":["https://openalex.org/W1494163043","https://openalex.org/W1497910784","https://openalex.org/W1965749137","https://openalex.org/W1966236704","https://openalex.org/W1974525150","https://openalex.org/W2030423480","https://openalex.org/W2049848090","https://openalex.org/W2069092055","https://openalex.org/W2072500636","https://openalex.org/W2102540081"],"related_works":["https://openalex.org/W1991902748","https://openalex.org/W2051533026","https://openalex.org/W4285722889","https://openalex.org/W2963377591","https://openalex.org/W2383221329","https://openalex.org/W2062690431","https://openalex.org/W2470850800","https://openalex.org/W46293795","https://openalex.org/W1982051704","https://openalex.org/W2045738033"],"abstract_inverted_index":{"Two":[0],"fast":[1],"algorithms":[2],"for":[3,53],"enclosing":[4],"all":[5],"eigenvalues":[6,27],"and":[7,21,31,42],"invariant":[8,22],"subspaces":[9,23],"in":[10],"generalized":[11],"eigenvalue":[12,45],"problems":[13],"are":[14,24,28],"proposed.":[15],"In":[16],"these":[17],"algorithms,":[18],"individual":[19],"eigenvectors":[20],"enclosed":[25],"when":[26],"well":[29],"separated":[30],"closely":[32],"clustered,":[33],"respectively.":[34],"The":[35,47],"first":[36],"algorithm":[37,49],"involves":[38],"only":[39],"cubic":[40],"complexity":[41],"automatically":[43],"determines":[44],"clusters.":[46],"second":[48],"is":[50],"applicable":[51],"even":[52],"defective":[54],"eigenvalues.":[55],"Numerical":[56],"results":[57],"show":[58],"the":[59,62],"properties":[60],"of":[61],"proposed":[63],"algorithms.":[64]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
