{"id":"https://openalex.org/W2108138101","doi":"https://doi.org/10.1137/060676489","title":"Efficient MATLAB Computations with Sparse and Factored Tensors","display_name":"Efficient MATLAB Computations with Sparse and Factored Tensors","publication_year":2007,"publication_date":"2007-12-07","ids":{"openalex":"https://openalex.org/W2108138101","doi":"https://doi.org/10.1137/060676489","mag":"2108138101"},"language":"en","primary_location":{"id":"doi:10.1137/060676489","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676489","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5110127240","display_name":"Brett W. Bader","orcid":null},"institutions":[{"id":"https://openalex.org/I139351228","display_name":"Office of Scientific and Technical Information","ror":"https://ror.org/031478740","country_code":"US","type":"government","lineage":["https://openalex.org/I1330989302","https://openalex.org/I139351228","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]},{"id":"https://openalex.org/I4210108489","display_name":"National Technical Information Service","ror":"https://ror.org/01p92hb48","country_code":"US","type":"government","lineage":["https://openalex.org/I1343035065","https://openalex.org/I4210108489"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Brett W. Bader","raw_affiliation_strings":["Computational Science and Mathematics Research Department Sandia National Laboratories Livermore, CA 94550-9159","Applied Computational Methods Department Sandia National Laboratories Albuquerque, NM 87185-0316","Department of Energy Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831","Department of Commerce National Technical Information Service 5285 Port Royal Rd Springfield, VA 22161"],"affiliations":[{"raw_affiliation_string":"Computational Science and Mathematics Research Department Sandia National Laboratories Livermore, CA 94550-9159","institution_ids":["https://openalex.org/I192454743"]},{"raw_affiliation_string":"Applied Computational Methods Department Sandia National Laboratories Albuquerque, NM 87185-0316","institution_ids":["https://openalex.org/I192454743"]},{"raw_affiliation_string":"Department of Energy Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831","institution_ids":["https://openalex.org/I139351228"]},{"raw_affiliation_string":"Department of Commerce National Technical Information Service 5285 Port Royal Rd Springfield, VA 22161","institution_ids":["https://openalex.org/I4210108489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039127251","display_name":"Tamara G. Kolda","orcid":"https://orcid.org/0000-0003-4176-2493"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tamara G. Kolda","raw_affiliation_strings":["SANDIA NATIONAL LABORATORIES, LIVERMORE, CA"],"affiliations":[{"raw_affiliation_string":"SANDIA NATIONAL LABORATORIES, LIVERMORE, CA","institution_ids":["https://openalex.org/I192454743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110127240"],"corresponding_institution_ids":["https://openalex.org/I139351228","https://openalex.org/I192454743","https://openalex.org/I4210108489"],"apc_list":null,"apc_paid":null,"fwci":12.9346,"has_fulltext":false,"cited_by_count":489,"citation_normalized_percentile":{"value":0.99378882,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"30","issue":"1","first_page":"205","last_page":"231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9516000151634216,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9429000020027161,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/tensor","display_name":"Tensor (intrinsic definition)","score":0.770869791507721},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6379407644271851},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.5510207414627075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5453571081161499},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5146997570991516},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.49230921268463135},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.4809255301952362},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4641979932785034},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4584382176399231},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45682528614997864},{"id":"https://openalex.org/keywords/tensor-product-of-hilbert-spaces","display_name":"Tensor product of Hilbert spaces","score":0.4488879442214966},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"Tensor contraction","score":0.44715026021003723},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.43547526001930237},{"id":"https://openalex.org/keywords/tucker-decomposition","display_name":"Tucker decomposition","score":0.41511115431785583},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4058690667152405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3964313864707947},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20111364126205444},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"Tensor decomposition","score":0.1898714303970337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1373620629310608},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13556748628616333}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.770869791507721},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6379407644271851},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.5510207414627075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5453571081161499},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5146997570991516},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.49230921268463135},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4809255301952362},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4641979932785034},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4584382176399231},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45682528614997864},{"id":"https://openalex.org/C93776189","wikidata":"https://www.wikidata.org/wiki/Q1404488","display_name":"Tensor product of Hilbert spaces","level":4,"score":0.4488879442214966},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.44715026021003723},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.43547526001930237},{"id":"https://openalex.org/C42704193","wikidata":"https://www.wikidata.org/wiki/Q7851097","display_name":"Tucker decomposition","level":4,"score":0.41511115431785583},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4058690667152405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3964313864707947},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20111364126205444},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.1898714303970337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1373620629310608},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13556748628616333},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060676489","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676489","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.8658","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.8658","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2006/067592.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.133.2206","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.133.2206","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://csmr.ca.sandia.gov/~tgkolda/pubs/bibtgkfiles/SIAM-67648.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3821936529","display_name":null,"funder_award_id":"Sandia","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W18434110","https://openalex.org/W137381930","https://openalex.org/W1489840835","https://openalex.org/W1506342804","https://openalex.org/W1529395041","https://openalex.org/W1529395305","https://openalex.org/W1589632425","https://openalex.org/W1848715260","https://openalex.org/W1963826206","https://openalex.org/W1977100800","https://openalex.org/W1978376511","https://openalex.org/W1978484662","https://openalex.org/W1978632288","https://openalex.org/W1983304143","https://openalex.org/W1986326495","https://openalex.org/W1986942951","https://openalex.org/W1991042426","https://openalex.org/W2000215628","https://openalex.org/W2002598080","https://openalex.org/W2006412395","https://openalex.org/W2007259720","https://openalex.org/W2013912476","https://openalex.org/W2018282388","https://openalex.org/W2027559251","https://openalex.org/W2035061066","https://openalex.org/W2037271374","https://openalex.org/W2037360998","https://openalex.org/W2042901969","https://openalex.org/W2047680880","https://openalex.org/W2057503509","https://openalex.org/W2069610307","https://openalex.org/W2071696173","https://openalex.org/W2073469810","https://openalex.org/W2079860873","https://openalex.org/W2089079408","https://openalex.org/W2092978222","https://openalex.org/W2093680667","https://openalex.org/W2097556710","https://openalex.org/W2111363262","https://openalex.org/W2113055885","https://openalex.org/W2113722075","https://openalex.org/W2119741678","https://openalex.org/W2121739212","https://openalex.org/W2122960905","https://openalex.org/W2124727221","https://openalex.org/W2135666716","https://openalex.org/W2136618620","https://openalex.org/W2137161964","https://openalex.org/W2147243899","https://openalex.org/W2150588270","https://openalex.org/W2167372553","https://openalex.org/W4229696524"],"related_works":["https://openalex.org/W2186765725","https://openalex.org/W2947494864","https://openalex.org/W2403348579","https://openalex.org/W2948436065","https://openalex.org/W2999609280","https://openalex.org/W2910590202","https://openalex.org/W2018969011","https://openalex.org/W2981910625","https://openalex.org/W2140205332","https://openalex.org/W4206901590"],"abstract_inverted_index":{"In":[0],"this":[1,59,176],"paper,":[2],"the":[3,34,37,41,55,79,102,130,139,142,145,150,153,168,172,181],"term":[4],"tensor":[5,69,97,107,125],"refers":[6],"simply":[7],"to":[8,68],"a":[9,105,117,123],"multidimensional":[10],"or":[11,114],"N-way":[12],"array,":[13],"and":[14,25,53,116,122,156],"we":[15,28,73,157],"consider":[16,91],"how":[17],"specially":[18],"structured":[19],"tensors":[20,49],"allow":[21],"for":[22,61,184],"efficient":[23],"storage":[24,143,151],"computation.":[26],"First,":[27],"study":[29,74],"sparse":[30,48],"tensors,":[31,76],"which":[32,77],"have":[33,78],"property":[35,80],"that":[36,81,159],"vast":[38],"majority":[39],"of":[40,58,104,132,144,152,171],"elements":[42],"are":[43,136,178],"zero.":[44],"We":[45,90,135],"propose":[46],"storing":[47],"using":[50,166],"coordinate":[51],"format":[52],"describe":[54],"computational":[56],"efficiency":[57],"scheme":[60],"various":[62],"mathematical":[63],"operations,":[64],"including":[65],"those":[66],"typical":[67],"decomposition":[70],"algorithms.":[71],"Second,":[72],"factored":[75],"they":[82],"can":[83,98,126,163],"be":[84,99,111,127,164],"assembled":[85],"from":[86],"more":[87],"basic":[88],"components.":[89,169],"two":[92],"specific":[93],"types:":[94],"A":[95],"Tucker":[96],"expressed":[100,128],"as":[101,129],"product":[103],"core":[106],"(which":[108],"itself":[109],"may":[110],"dense,":[112],"sparse,":[113],"factored)":[115],"matrix":[118],"along":[119],"each":[120],"mode,":[121],"Kruskal":[124],"sum":[131],"rank-1":[133],"tensors.":[134],"interested":[137],"in":[138,175,180],"case":[140],"where":[141],"components":[146],"is":[147],"less":[148],"than":[149],"full":[154],"tensor,":[155],"demonstrate":[158],"many":[160],"elementary":[161],"operations":[162],"computed":[165],"only":[167],"All":[170],"efficiencies":[173],"described":[174],"paper":[177],"implemented":[179],"Tensor":[182],"Toolbox":[183],"MATLAB.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":27},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":41},{"year":2019,"cited_by_count":46},{"year":2018,"cited_by_count":58},{"year":2017,"cited_by_count":33},{"year":2016,"cited_by_count":25},{"year":2015,"cited_by_count":31},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":21}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}