{"id":"https://openalex.org/W2242384245","doi":"https://doi.org/10.1137/15m1010890","title":"Successive Rank-One Approximations for Nearly Orthogonally Decomposable Symmetric Tensors","display_name":"Successive Rank-One Approximations for Nearly Orthogonally Decomposable Symmetric Tensors","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2242384245","doi":"https://doi.org/10.1137/15m1010890","mag":"2242384245"},"language":"en","primary_location":{"id":"doi:10.1137/15m1010890","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1010890","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1705.10404","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Cun Mu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cun Mu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Daniel Hsu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Hsu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Donald Goldfarb","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Donald Goldfarb","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5358,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.61167513,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"36","issue":"4","first_page":"1638","last_page":"1659"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9876000285148621,"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":0.9876000285148621,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.0044999998062849045,"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"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.002199999988079071,"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/symmetric-tensor","display_name":"Symmetric tensor","score":0.6610999703407288},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6401000022888184},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"Tensor decomposition","score":0.5575000047683716},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5192999839782715},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4740000069141388},{"id":"https://openalex.org/keywords/cartesian-tensor","display_name":"Cartesian tensor","score":0.4408000111579895},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4205000102519989},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4101000130176544},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.40470001101493835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8295999765396118},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.6610999703407288},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6401000022888184},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.5575000047683716},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5192999839782715},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4740000069141388},{"id":"https://openalex.org/C64835786","wikidata":"https://www.wikidata.org/wiki/Q17004583","display_name":"Cartesian tensor","level":5,"score":0.4408000111579895},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4097999930381775},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.40470001101493835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35589998960494995},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.35120001435279846},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C130956294","wikidata":"https://www.wikidata.org/wiki/Q2101158","display_name":"Polar decomposition","level":3,"score":0.32519999146461487},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.31439998745918274},{"id":"https://openalex.org/C158158286","wikidata":"https://www.wikidata.org/wiki/Q9009080","display_name":"Invariants of tensors","level":3,"score":0.30820000171661377},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C148125525","wikidata":"https://www.wikidata.org/wiki/Q904927","display_name":"Tensor density","level":4,"score":0.288100004196167},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27129998803138733},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1010890","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1010890","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:arXiv.org:1705.10404","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1705.10404","pdf_url":"https://arxiv.org/pdf/1705.10404","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1705.10404","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1705.10404","pdf_url":"https://arxiv.org/pdf/1705.10404","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4058019553","display_name":"Fast First-Order Methods for Large-Scale Structured and Sparse Optimization","funder_award_id":"1016571","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8415863282","display_name":"CIF: Small: Structured Signal Modeling via Nonconvex Optimization","funder_award_id":"1527809","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1824940946","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1970136394","https://openalex.org/W1970377488","https://openalex.org/W1978376511","https://openalex.org/W1981566278","https://openalex.org/W1986370957","https://openalex.org/W2001916104","https://openalex.org/W2002598080","https://openalex.org/W2004026774","https://openalex.org/W2007036852","https://openalex.org/W2018282388","https://openalex.org/W2024165284","https://openalex.org/W2037049667","https://openalex.org/W2048050794","https://openalex.org/W2057503509","https://openalex.org/W2069287942","https://openalex.org/W2070028074","https://openalex.org/W2079705627","https://openalex.org/W2081106919","https://openalex.org/W2088221456","https://openalex.org/W2090799283","https://openalex.org/W2090967418","https://openalex.org/W2099741732","https://openalex.org/W2112451877","https://openalex.org/W2112702842","https://openalex.org/W2122761035","https://openalex.org/W2126381689","https://openalex.org/W2128762995","https://openalex.org/W2132267493","https://openalex.org/W2569661359"],"related_works":[],"abstract_inverted_index":{"Many":[0],"idealized":[1],"problems":[2],"in":[3,112],"signal":[4],"processing,":[5],"machine":[6],"learning,":[7],"and":[8,26,46,54,80],"statistics":[9],"can":[10,87,118],"be":[11,89,92],"reduced":[12],"to":[13,48,91,155],"the":[14,18,34,37,65,73,84,103,113,122,127,135,141,148,157],"problem":[15],"of":[16,22,57,115,126],"finding":[17],"symmetric":[19,25,98,123],"canonical":[20,124],"decomposition":[21,52,125],"an":[23],"underlying":[24,104,128],"orthogonally":[27],"decomposable":[28],"(SOD)":[29],"tensor.":[30,106,129],"Drawing":[31],"inspiration":[32],"from":[33,77,102],"matrix":[35],"case,":[36],"successive":[38],"rank-one":[39,67],"approximation":[40,68,142],"(SROA)":[41],"scheme":[42],"has":[43],"been":[44,62],"proposed":[45],"shown":[47,132],"yield":[49],"this":[50],"tensor":[51,66,86,99],"exactly,":[53],"a":[55,93,97],"plethora":[56],"numerical":[58],"methods":[59],"have":[60],"thus":[61],"developed":[63],"for":[64],"problem.":[69],"In":[70],"practice,":[71],"however,":[72],"inevitable":[74],"errors":[75,143],"(say)":[76],"estimation,":[78],"computation,":[79],"modeling":[81],"necessitate":[82],"that":[83,110,133],"input":[85],"only":[88],"assumed":[90],"nearly":[94],"SOD":[95,105],"tensor---i.e.,":[96],"slightly":[100],"perturbed":[101],"This":[107],"paper":[108],"shows":[109],"even":[111],"presence":[114],"perturbation,":[116],"SROA":[117],"still":[119],"robustly":[120],"recover":[121],"It":[130],"is":[131,138],"when":[134],"perturbation":[136],"error":[137],"small":[139],"enough,":[140],"do":[144],"not":[145],"accumulate":[146],"with":[147],"iteration":[149],"number.":[150],"Numerical":[151],"results":[152],"are":[153],"presented":[154],"support":[156],"theoretical":[158],"findings.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2016-06-24T00:00:00"}
