{"id":"https://openalex.org/W2972630054","doi":"https://doi.org/10.1137/18m1208101","title":"Numerical Computation for Orthogonal Low-Rank Approximation of Tensors","display_name":"Numerical Computation for Orthogonal Low-Rank Approximation of Tensors","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2972630054","doi":"https://doi.org/10.1137/18m1208101","mag":"2972630054"},"language":"en","primary_location":{"id":"doi:10.1137/18m1208101","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1208101","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/A5022948886","display_name":"Yu Guan","orcid":"https://orcid.org/0000-0002-0864-2222"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu Guan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102966756","display_name":"Delin Chu","orcid":"https://orcid.org/0000-0001-7736-7490"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Delin Chu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7736-7490","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6493,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.90441176,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"1047","last_page":"1065"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.986299991607666,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9764999747276306,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8065742254257202},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.7233617305755615},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.6801871657371521},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.6363124847412109},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5983304977416992},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.5477123856544495},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5250603556632996},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.510648787021637},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5025348663330078},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.5016627311706543},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4469168782234192},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44483983516693115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36252522468566895},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2942177653312683},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2728756070137024},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2036944031715393},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.1746114194393158},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.17026695609092712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08358004689216614}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8065742254257202},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.7233617305755615},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.6801871657371521},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.6363124847412109},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5983304977416992},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.5477123856544495},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5250603556632996},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.510648787021637},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5025348663330078},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.5016627311706543},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4469168782234192},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44483983516693115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36252522468566895},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2942177653312683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2728756070137024},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2036944031715393},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.1746114194393158},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.17026695609092712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08358004689216614},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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:10.1137/18m1208101","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1208101","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":40,"referenced_works":["https://openalex.org/W1754171797","https://openalex.org/W1963826206","https://openalex.org/W1968061328","https://openalex.org/W1978165409","https://openalex.org/W1978376511","https://openalex.org/W1978632288","https://openalex.org/W1999175670","https://openalex.org/W2000215628","https://openalex.org/W2001756763","https://openalex.org/W2002598080","https://openalex.org/W2004026774","https://openalex.org/W2013912476","https://openalex.org/W2018282388","https://openalex.org/W2019219605","https://openalex.org/W2021958990","https://openalex.org/W2024165284","https://openalex.org/W2024938971","https://openalex.org/W2030699645","https://openalex.org/W2065243655","https://openalex.org/W2073389244","https://openalex.org/W2075184363","https://openalex.org/W2076459794","https://openalex.org/W2076603483","https://openalex.org/W2079407403","https://openalex.org/W2082658029","https://openalex.org/W2087648855","https://openalex.org/W2088307891","https://openalex.org/W2099228589","https://openalex.org/W2101641981","https://openalex.org/W2112702842","https://openalex.org/W2115139877","https://openalex.org/W2132220618","https://openalex.org/W2132267493","https://openalex.org/W2136023375","https://openalex.org/W2139457438","https://openalex.org/W2154908766","https://openalex.org/W2515303911","https://openalex.org/W2626282436","https://openalex.org/W2806658157","https://openalex.org/W2810771934"],"related_works":["https://openalex.org/W2021905036","https://openalex.org/W2013801824","https://openalex.org/W1529452180","https://openalex.org/W1496788307","https://openalex.org/W2149054915","https://openalex.org/W1591253575","https://openalex.org/W2108939823","https://openalex.org/W3178433292","https://openalex.org/W2363331359","https://openalex.org/W1981917738"],"abstract_inverted_index":{"In":[0],"this":[1,88],"paper":[2],"we":[3,91],"study":[4],"the":[5,13,17,33,78,105,112],"orthogonal":[6,35],"low-rank":[7,36,40],"approximation":[8,37,41],"problem":[9],"of":[10,69,80,111,118],"tensors":[11],"in":[12,16,50],"general":[14],"setting":[15],"sense":[18],"that":[19,66],"more":[20,70],"than":[21,71],"one":[22,72],"matrix":[23],"factor":[24,74],"is":[25,121,131],"required":[26,106],"to":[27],"be":[28],"mutually":[29],"orthonormal,":[30],"which":[31],"includes":[32],"completely":[34],"and":[38,53,103,127,130],"semiorthogonal":[39],"as":[42],"two":[43,100],"special":[44],"cases.":[45],"It":[46],"has":[47],"been":[48],"addressed":[49],"[L.":[51],"Wang":[52],"M.":[54],"T.":[55],"Chu,":[56],"SIAM":[57],"J.":[58],"Matrix":[59],"Anal.":[60],"Appl.,":[61],"35":[62],"(2014),":[63],"pp.":[64],"1058--1072]":[65],"\u201cthe":[67],"question":[68,90],"semi-orthogonal":[73],"matrix,":[75],"except":[76],"for":[77,123],"case":[79],"complete":[81],"orthogonality,":[82],"remains":[83],"open.\u201d":[84],"To":[85],"deal":[86],"with":[87],"open":[89],"present":[92],"an":[93],"SVD-based":[94,97],"algorithm.":[95],"Our":[96],"algorithm":[98,120],"updates":[99],"vectors":[101],"simultaneously":[102],"maintains":[104],"orthogonality":[107],"conditions":[108],"by":[109,133],"means":[110],"polar":[113],"decomposition.":[114],"The":[115],"convergence":[116],"behavior":[117],"our":[119],"analyzed":[122],"both":[124],"objective":[125],"function":[126],"iterates":[128],"themselves":[129],"illustrated":[132],"numerical":[134],"experiments.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
