{"id":"https://openalex.org/W3105925603","doi":"https://doi.org/10.1137/140983410","title":"Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format","display_name":"Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W3105925603","doi":"https://doi.org/10.1137/140983410","mag":"3105925603"},"language":"en","primary_location":{"id":"doi:10.1137/140983410","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140983410","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/1410.6895","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042263650","display_name":"Namgil Lee","orcid":"https://orcid.org/0000-0003-0593-9028"},"institutions":[{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Namgil Lee","raw_affiliation_strings":["Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-shi, Saitama 3510198, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-shi, Saitama 3510198, Japan","institution_ids":["https://openalex.org/I2800939219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018676117","display_name":"Andrzej Cichocki","orcid":"https://orcid.org/0000-0002-8364-7226"},"institutions":[{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Andrzej Cichocki","raw_affiliation_strings":["Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-shi, Saitama 3510198, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-shi, Saitama 3510198, Japan","institution_ids":["https://openalex.org/I2800939219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042263650"],"corresponding_institution_ids":["https://openalex.org/I2800939219"],"apc_list":null,"apc_paid":null,"fwci":1.9343,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.85316456,"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":"994","last_page":"1014"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9854000210762024,"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":0.9004999995231628,"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/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8521397709846497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.741481363773346},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6869835257530212},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6387474536895752},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5746637582778931},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5452611446380615},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4625365734100342},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4406070113182068},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.4403928816318512},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4065096974372864},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37728387117385864},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.255585640668869},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16805219650268555}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8521397709846497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741481363773346},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6869835257530212},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6387474536895752},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5746637582778931},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5452611446380615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4625365734100342},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4406070113182068},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.4403928816318512},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4065096974372864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37728387117385864},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.255585640668869},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16805219650268555},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140983410","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140983410","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:1410.6895","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1410.6895","pdf_url":"https://arxiv.org/pdf/1410.6895","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:1410.6895","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1410.6895","pdf_url":"https://arxiv.org/pdf/1410.6895","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1246381107","https://openalex.org/W1531635645","https://openalex.org/W1570334424","https://openalex.org/W1832467415","https://openalex.org/W1952127226","https://openalex.org/W1963973528","https://openalex.org/W1967077133","https://openalex.org/W1967538125","https://openalex.org/W1968119930","https://openalex.org/W1968157422","https://openalex.org/W1975172027","https://openalex.org/W1980428773","https://openalex.org/W1983543686","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W1996869553","https://openalex.org/W1998258511","https://openalex.org/W2001518794","https://openalex.org/W2008657736","https://openalex.org/W2013912476","https://openalex.org/W2016407890","https://openalex.org/W2019741430","https://openalex.org/W2024165284","https://openalex.org/W2031216664","https://openalex.org/W2036133196","https://openalex.org/W2036604884","https://openalex.org/W2038198231","https://openalex.org/W2038920431","https://openalex.org/W2048459485","https://openalex.org/W2051142108","https://openalex.org/W2063125621","https://openalex.org/W2067067855","https://openalex.org/W2088025933","https://openalex.org/W2088739747","https://openalex.org/W2119412403","https://openalex.org/W2122816100","https://openalex.org/W2132267493","https://openalex.org/W2133512121","https://openalex.org/W2133884101","https://openalex.org/W2952134683","https://openalex.org/W2952557657","https://openalex.org/W3103713775","https://openalex.org/W4253140037","https://openalex.org/W4288938614","https://openalex.org/W4301491118","https://openalex.org/W4394669802"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W1607100495","https://openalex.org/W2010100052","https://openalex.org/W1990844505","https://openalex.org/W2148568324","https://openalex.org/W4378770618","https://openalex.org/W4386721910","https://openalex.org/W2038393145","https://openalex.org/W2690537872"],"abstract_inverted_index":{"We":[0],"propose":[1],"new":[2],"algorithms":[3,27,235,238],"for":[4,43,169,200,240],"singular":[5,37,41,74,105,185,224],"value":[6],"decomposition":[7],"(SVD)":[8],"of":[9,55,127,144,172,204,215,232],"large-scale":[10,44,113],"matrices":[11,46,174],"based":[12],"on":[13],"a":[14,30,49,180,205,221],"low-rank":[15,78],"tensor":[16,21,126],"approximation":[17,162],"technique":[18],"called":[19,86],"the":[20,56,62,66,70,73,87,101,128,145,153,177,213,216,230],"train":[22],"(TT)":[23],"format.":[24,51],"The":[25,52,81,141,194,209],"proposed":[26,57,82,195,217],"can":[28,132,159],"compute":[29,100],"few":[31,222],"extreme":[32,223],"(i.e.,":[33],"largest":[34],"or":[35],"smallest)":[36],"values":[38,225],"and":[39,72,93,103,123,188,191,226,236],"corresponding":[40],"vectors":[42,75,106],"structured":[45],"given":[47],"in":[48,219],"TT":[50,79,110,130,147],"computational":[53],"complexity":[54],"methods":[58,196,218],"scales":[59],"logarithmically":[60],"with":[61,183,229],"matrix":[63,71,182],"size":[64],"under":[65],"assumption":[67],"that":[68,157],"both":[69],"admit":[76],"approximate":[77],"decompositions.":[80,111],"methods,":[83],"which":[84],"are":[85,149,167,197],"alternating":[88,95],"least":[89,96],"squares":[90,97],"SVD":[91,98,139,234],"(ALS-SVD)":[92],"modified":[94],"(MALS-SVD),":[99],"left":[102],"right":[104],"approximately":[107],"through":[108],"block":[109,129,146],"A":[112],"optimization":[114,121],"problem":[115],"is":[116],"reduced":[117],"to":[118],"sequential":[119],"small-scale":[120],"problems,":[122],"each":[124],"core":[125],"decompositions":[131,148],"be":[133],"updated":[134],"by":[135],"applying":[136],"any":[137],"standard":[138,233],"method.":[140],"optimal":[142],"ranks":[143],"determined":[150],"adaptively":[151],"during":[152],"iteration":[154],"process,":[155],"so":[156],"we":[158],"achieve":[160],"high":[161],"accuracy.":[163],"Extensive":[164],"numerical":[165],"simulations":[166],"conducted":[168],"several":[170],"types":[171],"TT-structured":[173],"such":[175],"as":[176],"Hilbert":[178],"matrix,":[179],"random":[181],"prescribed":[184],"values,":[186],"Hankel":[187],"Toeplitz":[189],"matrices,":[190],"tridiagonal":[192],"matrices.":[193],"also":[198],"applied":[199],"computing":[201],"stationary":[202],"solutions":[203],"partial":[206],"differential":[207],"equation.":[208],"experimental":[210],"results":[211],"demonstrate":[212],"effectiveness":[214],"estimating":[220],"vectors,":[227],"compared":[228],"performance":[231],"TT-based":[237],"developed":[239],"symmetric":[241],"eigenvalue":[242],"decomposition.":[243]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2020-11-23T00:00:00"}