{"id":"https://openalex.org/W2089637519","doi":"https://doi.org/10.1002/nla.765","title":"Fast truncation of mode ranks for bilinear tensor operations","display_name":"Fast truncation of mode ranks for bilinear tensor operations","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2089637519","doi":"https://doi.org/10.1002/nla.765","mag":"2089637519"},"language":"en","primary_location":{"id":"doi:10.1002/nla.765","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.765","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.765","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.765","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"D. V. Savostyanov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086928","display_name":"Institute of Numerical Mathematics","ror":"https://ror.org/00520ey40","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210086928","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"D. V. Savostyanov","raw_affiliation_strings":["Institute of Numerical Mathematics RAS, Gubkina 8, 119333 Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Numerical Mathematics RAS, Gubkina 8, 119333 Moscow, Russia","institution_ids":["https://openalex.org/I4210086928"]}]},{"author_position":"middle","author":{"id":null,"display_name":"E. E. Tyrtyshnikov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086928","display_name":"Institute of Numerical Mathematics","ror":"https://ror.org/00520ey40","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210086928","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"E. E. Tyrtyshnikov","raw_affiliation_strings":["Institute of Numerical Mathematics RAS, Gubkina 8, 119333 Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Numerical Mathematics RAS, Gubkina 8, 119333 Moscow, Russia","institution_ids":["https://openalex.org/I4210086928"]}]},{"author_position":"last","author":{"id":null,"display_name":"N. L. Zamarashkin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086928","display_name":"Institute of Numerical Mathematics","ror":"https://ror.org/00520ey40","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210086928","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"N. L. Zamarashkin","raw_affiliation_strings":["Institute of Numerical Mathematics RAS, Gubkina 8, 119333 Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Numerical Mathematics RAS, Gubkina 8, 119333 Moscow, Russia","institution_ids":["https://openalex.org/I4210086928"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210086928"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.5679,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.62345679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"1","first_page":"103","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9279999732971191,"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":0.9279999732971191,"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":0.00989999994635582,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.00419999985024333,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.7085999846458435},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6306999921798706},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.5906999707221985},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.588100016117096},{"id":"https://openalex.org/keywords/bilinear-transform","display_name":"Bilinear transform","score":0.5619000196456909},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.511900007724762},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.4715000092983246},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4618000090122223}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252000212669373},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.7085999846458435},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6306999921798706},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.5906999707221985},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.588100016117096},{"id":"https://openalex.org/C109786386","wikidata":"https://www.wikidata.org/wiki/Q861804","display_name":"Bilinear transform","level":4,"score":0.5619000196456909},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.511900007724762},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4788999855518341},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.4715000092983246},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4618000090122223},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.46149998903274536},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.4401000142097473},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43290001153945923},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.2946000099182129},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2842999994754791},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.27149999141693115},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/nla.765","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.765","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.765","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1004.4919","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1004.4919","pdf_url":"https://arxiv.org/pdf/1004.4919","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},{"id":"pmh:oai:pure.atira.dk:openaire/e21ecef7-ff50-4646-8ff1-045b8f74bdd4","is_oa":true,"landing_page_url":"https://research.brighton.ac.uk/en/publications/e21ecef7-ff50-4646-8ff1-045b8f74bdd4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401758","display_name":"University of Brighton Repository (University of Brighton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71637028","host_organization_name":"University of Brighton","host_organization_lineage":["https://openalex.org/I71637028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Savostyanov, D V, Tyrtyshnikov, E E & Zamarashkin, N L 2012, 'Fast truncation of mode ranks for bilinear tensor operations', Numerical Linear Algebra with Applications, vol. 19, no. 1, pp. 103-111. https://doi.org/10.1002/nla.765","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1002/nla.765","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.765","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.765","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2089637519.pdf","grobid_xml":"https://content.openalex.org/works/W2089637519.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W194074478","https://openalex.org/W1963826206","https://openalex.org/W1969720662","https://openalex.org/W1980906180","https://openalex.org/W1983101562","https://openalex.org/W1991042426","https://openalex.org/W1991547453","https://openalex.org/W2000215628","https://openalex.org/W2002630401","https://openalex.org/W2013912476","https://openalex.org/W2018282388","https://openalex.org/W2024938971","https://openalex.org/W2032402705","https://openalex.org/W2055881647","https://openalex.org/W2078465266","https://openalex.org/W2078789945","https://openalex.org/W2117730583","https://openalex.org/W2132267493","https://openalex.org/W2258054274","https://openalex.org/W2496219407","https://openalex.org/W4231187174","https://openalex.org/W4301491118"],"related_works":[],"abstract_inverted_index":{"SUMMARY":[0],"We":[1,79,106],"propose":[2],"a":[3,14],"fast":[4],"algorithm":[5,52],"for":[6,84,103],"mode":[7,33,37],"rank":[8],"truncation":[9],"of":[10,13,59,65,75,87,91,111,121],"the":[11,21,27,30,41,56,63,66,76,81,85,88,92,109,112,122,130],"result":[12,31],"bilinear":[15],"operation":[16],"on":[17,55],"3\u2010tensors":[18],"given":[19],"in":[20],"Tucker":[22,68,114],"or":[23],"canonical":[24],"form.":[25],"If":[26],"arguments":[28],"and":[29,36,62,95,116],"have":[32],"sizes":[34],"n":[35],"ranks":[38],"r":[39,48],",":[40],"computation":[42],"costs":[43],"(":[44],"nr":[45],"3":[46],"+":[47],"4":[49],").":[50],"The":[51],"is":[53,70],"based":[54],"cross":[57],"approximation":[58,69,115],"Gram":[60],"matrices,":[61],"accuracy":[64,110],"resulted":[67,113],"limited":[71],"by":[72],"square":[73,90],"root":[74],"machine":[77,131],"precision.":[78,132],"apply":[80],"proposed":[82],"algorithms":[83],"evaluation":[86],"Hadamard":[89],"electron":[93],"density":[94],"demonstrate":[96],"that":[97,118],"it":[98,126],"outperforms":[99],"previously":[100],"used":[101],"methods":[102],"this":[104],"purpose.":[105],"also":[107],"check":[108],"show":[117],"one":[119],"iteration":[120],"Tucker\u2010ALS":[123],"method":[124],"improves":[125],"almost":[127],"up":[128],"to":[129],"Copyright":[133],"\u00a9":[134],"2011":[135],"John":[136],"Wiley":[137],"&":[138],"Sons,":[139],"Ltd.":[140]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2016-06-24T00:00:00"}