{"id":"https://openalex.org/W2981381730","doi":"https://doi.org/10.1080/10556788.2019.1678034","title":"Symmetric rank-1 approximation of symmetric high-order tensors","display_name":"Symmetric rank-1 approximation of symmetric high-order tensors","publication_year":2019,"publication_date":"2019-10-21","ids":{"openalex":"https://openalex.org/W2981381730","doi":"https://doi.org/10.1080/10556788.2019.1678034","mag":"2981381730"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2019.1678034","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1678034","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","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/A5079688232","display_name":"Leqin Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Leqin Wu","raw_affiliation_strings":["Department of Information Science and Technology, Jinan University China, Guangzhou, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Science and Technology, Jinan University China, Guangzhou, People's Republic of China","institution_ids":["https://openalex.org/I159948400"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100352246","display_name":"Xin Liu","orcid":"https://orcid.org/0000-0002-5705-0805"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin Liu","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, Beijing, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-5705-0805","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006127137","display_name":"Zaiwen Wen","orcid":"https://orcid.org/0000-0003-1762-0671"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zaiwen Wen","raw_affiliation_strings":["Beijing International Center for Mathematical Research, Peking University, Beijing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing International Center for Mathematical Research, Peking University, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100352246"],"corresponding_institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":0.1471,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.35164835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"35","issue":"2","first_page":"416","last_page":"438"},"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":0.9743000268936157,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9718000292778015,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8492722511291504},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6500343084335327},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.6486369371414185},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5578746795654297},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4009025990962982},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3802558481693268},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32900676131248474},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1947978138923645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8492722511291504},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6500343084335327},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.6486369371414185},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5578746795654297},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4009025990962982},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3802558481693268},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32900676131248474},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1947978138923645},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2019.1678034","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1678034","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","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":32,"referenced_works":["https://openalex.org/W1507925093","https://openalex.org/W1824940946","https://openalex.org/W1863007351","https://openalex.org/W1969404979","https://openalex.org/W1973991444","https://openalex.org/W1986370957","https://openalex.org/W2018282388","https://openalex.org/W2020374088","https://openalex.org/W2024266080","https://openalex.org/W2026518586","https://openalex.org/W2027982384","https://openalex.org/W2031621232","https://openalex.org/W2039212488","https://openalex.org/W2070028074","https://openalex.org/W2083531734","https://openalex.org/W2084288381","https://openalex.org/W2088221456","https://openalex.org/W2090208105","https://openalex.org/W2090799283","https://openalex.org/W2113074910","https://openalex.org/W2116854630","https://openalex.org/W2165471068","https://openalex.org/W2176364383","https://openalex.org/W2204118584","https://openalex.org/W2462530370","https://openalex.org/W2950237760","https://openalex.org/W2964345672","https://openalex.org/W3022190075","https://openalex.org/W3098015574","https://openalex.org/W3143686696","https://openalex.org/W3213229115","https://openalex.org/W4230252983"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2088849544","https://openalex.org/W4234996786","https://openalex.org/W2017331178","https://openalex.org/W2991887548","https://openalex.org/W3102408541","https://openalex.org/W3098790080","https://openalex.org/W2964175299","https://openalex.org/W2153806284"],"abstract_inverted_index":{"Finding":[0],"the":[1,24,38,46],"symmetric":[2,8],"rank-1":[3],"approximation":[4],"to":[5,15,23,43,71],"a":[6,27,34],"given":[7],"tensor":[9],"is":[10,54,62],"an":[11],"important":[12],"problem":[13],"due":[14],"its":[16,20],"wide":[17],"applications":[18],"and":[19,68],"close":[21],"relationship":[22],"Z-eigenpair":[25],"of":[26,51],"tensor.":[28],"In":[29],"this":[30],"paper,":[31],"we":[32],"propose":[33],"method":[35],"based":[36],"on":[37],"proximal":[39],"alternating":[40],"linearized":[41],"minimization":[42],"directly":[44],"solve":[45],"optimization":[47],"problem.":[48],"Global":[49],"convergence":[50],"our":[52,60],"algorithm":[53,61],"established.":[55],"Numerical":[56],"experiments":[57],"show":[58],"that":[59],"very":[63],"competitive":[64],"in":[65],"speed,":[66],"accuracy":[67],"robustness":[69],"compared":[70],"other":[72],"state-of-the-art":[73],"methods.":[74]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}