{"id":"https://openalex.org/W1064128852","doi":"https://doi.org/10.1137/140975656","title":"Generalized Tensor Eigenvalue Problems","display_name":"Generalized Tensor Eigenvalue Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1064128852","doi":"https://doi.org/10.1137/140975656","mag":"1064128852"},"language":"en","primary_location":{"id":"doi:10.1137/140975656","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140975656","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/A5069964397","display_name":"Weiyang Ding","orcid":"https://orcid.org/0000-0003-3075-5781"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Weiyang Ding","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014988509","display_name":"Yimin Wei","orcid":"https://orcid.org/0000-0001-6192-0546"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yimin Wei","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069964397"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3609,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":{"value":0.88145315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"36","issue":"3","first_page":"1073","last_page":"1099"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9957000017166138,"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":0.9824000000953674,"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":0.8648715019226074},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6987967491149902},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6962921619415283},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6350465416908264},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5162680149078369},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5027942657470703},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4563712179660797},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4510025382041931},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4387107491493225},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3814922571182251},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3621164858341217},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.23775407671928406}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8648715019226074},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6987967491149902},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6962921619415283},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6350465416908264},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5162680149078369},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5027942657470703},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4563712179660797},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4510025382041931},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4387107491493225},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3814922571182251},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3621164858341217},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.23775407671928406},{"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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140975656","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140975656","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W658559791","https://openalex.org/W1656443807","https://openalex.org/W1793447552","https://openalex.org/W1944315015","https://openalex.org/W1951162345","https://openalex.org/W1971702983","https://openalex.org/W1979035610","https://openalex.org/W2012593053","https://openalex.org/W2013139982","https://openalex.org/W2020374088","https://openalex.org/W2031621232","https://openalex.org/W2040551015","https://openalex.org/W2041197939","https://openalex.org/W2044008067","https://openalex.org/W2046402929","https://openalex.org/W2048024795","https://openalex.org/W2070769763","https://openalex.org/W2078337493","https://openalex.org/W2084288381","https://openalex.org/W2090208105","https://openalex.org/W2095180325","https://openalex.org/W2109090100","https://openalex.org/W2120001551","https://openalex.org/W2140243727","https://openalex.org/W2312974704","https://openalex.org/W2964074814","https://openalex.org/W3105081413","https://openalex.org/W3148981562","https://openalex.org/W3199893329","https://openalex.org/W4243620103"],"related_works":["https://openalex.org/W2745406996","https://openalex.org/W2086589508","https://openalex.org/W2952501628","https://openalex.org/W1465116025","https://openalex.org/W2964145023","https://openalex.org/W2005900207","https://openalex.org/W2038494689","https://openalex.org/W2058866529","https://openalex.org/W2917317413","https://openalex.org/W2155866799"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"devoted":[3],"to":[4,36,64],"generalized":[5],"tensor":[6,21,37,63],"eigenvalue":[7],"problems.":[8],"We":[9],"focus":[10],"on":[11],"the":[12,17,41,45,48,51,57],"properties":[13],"and":[14],"perturbations":[15],"of":[16,19,60,68],"spectra":[18],"regular":[20],"pairs.":[22],"Employing":[23],"different":[24],"techniques,":[25],"we":[26],"extend":[27],"several":[28],"classical":[29],"results":[30,70],"from":[31],"matrices":[32],"or":[33],"matrix":[34],"pairs":[35],"pairs,":[38],"such":[39],"as":[40],"Gershgorin":[42],"circle":[43],"theorem,":[44,50,53],"Collatz--Wielandt":[46],"formula,":[47],"Bauer--Fike":[49],"Rayleigh--Ritz":[52],"backward":[54],"error":[55],"analysis,":[56],"componentwise":[58],"distance":[59],"a":[61],"nonsingular":[62],"singularity,":[65],"etc.":[66],"Some":[67],"these":[69],"preserve":[71],"their":[72],"original":[73],"forms,":[74],"while":[75],"others":[76],"change":[77],"when":[78],"being":[79],"extended.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}