{"id":"https://openalex.org/W2031621232","doi":"https://doi.org/10.1137/140962292","title":"All Real Eigenvalues of Symmetric Tensors","display_name":"All Real Eigenvalues of Symmetric Tensors","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2031621232","doi":"https://doi.org/10.1137/140962292","mag":"2031621232"},"language":"en","primary_location":{"id":"doi:10.1137/140962292","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140962292","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/A5057257613","display_name":"Chunfeng Cui","orcid":"https://orcid.org/0000-0002-6815-4060"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chun-Feng Cui","raw_affiliation_strings":["Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109187979","display_name":"Yu\u2010Hong Dai","orcid":"https://orcid.org/0000-0002-6932-9512"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu-Hong Dai","raw_affiliation_strings":["Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018024598","display_name":"Jiawang Nie","orcid":"https://orcid.org/0000-0003-2637-8274"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiawang Nie","raw_affiliation_strings":["Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057257613"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":5.3942,"has_fulltext":false,"cited_by_count":159,"citation_normalized_percentile":{"value":0.96588486,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"35","issue":"4","first_page":"1582","last_page":"1601"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9642999768257141,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9613999724388123,"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":0.859381914138794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8196716904640198},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6167131066322327},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6131587028503418},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5631802082061768},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5601760745048523},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5531995892524719},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42838963866233826},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33967339992523193},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33591991662979126},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3289351761341095},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1930803656578064},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.07364636659622192}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.859381914138794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8196716904640198},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6167131066322327},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6131587028503418},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5631802082061768},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5601760745048523},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5531995892524719},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42838963866233826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33967339992523193},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33591991662979126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3289351761341095},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1930803656578064},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.07364636659622192},{"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":2,"locations":[{"id":"doi:10.1137/140962292","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140962292","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.759.550","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.759.550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1403.3720.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1117093733","display_name":null,"funder_award_id":"1417985","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3471528664","display_name":null,"funder_award_id":"DMS-0844775","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4120529948","display_name":null,"funder_award_id":"DMS-1417985","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5506372858","display_name":"CAREER: Linear Matrix Inequality Representations in Optimization","funder_award_id":"0844775","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6799592476","display_name":null,"funder_award_id":"1133101","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8312901025","display_name":null,"funder_award_id":"1301016","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8467377261","display_name":null,"funder_award_id":"11301","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1546449335","https://openalex.org/W1602307574","https://openalex.org/W1944315015","https://openalex.org/W1967344706","https://openalex.org/W1981973750","https://openalex.org/W1986370957","https://openalex.org/W1993529825","https://openalex.org/W2007036852","https://openalex.org/W2020374088","https://openalex.org/W2024165284","https://openalex.org/W2052557161","https://openalex.org/W2057170710","https://openalex.org/W2067774845","https://openalex.org/W2070028074","https://openalex.org/W2082443028","https://openalex.org/W2084288381","https://openalex.org/W2088221456","https://openalex.org/W2090208105","https://openalex.org/W2090967418","https://openalex.org/W2118214857","https://openalex.org/W2150544307","https://openalex.org/W2155438968","https://openalex.org/W2204118584"],"related_works":["https://openalex.org/W3050972237","https://openalex.org/W3214531188","https://openalex.org/W4353081986","https://openalex.org/W2086589508","https://openalex.org/W1555881074","https://openalex.org/W2952501628","https://openalex.org/W2519254393","https://openalex.org/W2323625272","https://openalex.org/W3122498363","https://openalex.org/W3162816895"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"how":[3,88],"to":[4,10,55,86,89],"compute":[5],"all":[6,48],"real":[7,11,49],"eigenvalues,":[8],"associated":[9],"eigenvectors,":[12],"of":[13,79],"a":[14,31,43,76],"symmetric":[15],"tensor.":[16],"As":[17],"is":[18],"well":[19],"known,":[20],"the":[21,36,53,56],"largest":[22,54],"or":[23],"smallest":[24],"eigenvalue":[25,70],"can":[26,71],"be":[27,72],"found":[28],"by":[29,74],"solving":[30,75],"polynomial":[32,64],"optimization":[33],"problem,":[34],"while":[35],"other":[37],"middle":[38],"ones":[39],"cannot.":[40],"We":[41,66],"propose":[42],"new":[44],"approach":[45],"for":[46],"computing":[47],"eigenvalues":[50],"sequentially,":[51],"from":[52],"smallest.":[57],"It":[58],"uses":[59],"Jacobian":[60],"semidefinite":[61,80],"relaxations":[62],"in":[63],"optimization.":[65],"show":[67,87],"that":[68],"each":[69],"computed":[73],"finite":[77],"hierarchy":[78],"relaxations.":[81],"Numerical":[82],"experiments":[83],"are":[84],"presented":[85],"do":[90],"this.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
