{"id":"https://openalex.org/W4226036541","doi":"https://doi.org/10.1109/lsp.2022.3156870","title":"Canonical Polyadic Decomposition via the Generalized Schur Decomposition","display_name":"Canonical Polyadic Decomposition via the Generalized Schur Decomposition","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4226036541","doi":"https://doi.org/10.1109/lsp.2022.3156870"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2022.3156870","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2022.3156870","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/20.500.12942/691336","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017164422","display_name":"Eric Evert","orcid":"https://orcid.org/0000-0002-5488-8725"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Eric Evert","raw_affiliation_strings":["Department of Electrical Engineering, ESAT/- STADIUS, KU Leuven, Leuven, Belgium","Kulak, Kortrijk, Belgium","Group Science, Engineering and Technology, KU Leuven&#x2013"],"raw_orcid":"https://orcid.org/0000-0002-5488-8725","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, ESAT/- STADIUS, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Kulak, Kortrijk, Belgium","institution_ids":[]},{"raw_affiliation_string":"Group Science, Engineering and Technology, KU Leuven&#x2013","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049123030","display_name":"Michiel Vandecappelle","orcid":"https://orcid.org/0000-0001-6231-5313"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Michiel Vandecappelle","raw_affiliation_strings":["Department of Electrical Engineering, ESAT/- STADIUS, KU Leuven, Leuven, Belgium","Kulak, Kortrijk, Belgium","Group Science, Engineering and Technology, KU Leuven&#x2013"],"raw_orcid":"https://orcid.org/0000-0001-6231-5313","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, ESAT/- STADIUS, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Kulak, Kortrijk, Belgium","institution_ids":[]},{"raw_affiliation_string":"Group Science, Engineering and Technology, KU Leuven&#x2013","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009006026","display_name":"Lieven De Lathauwer","orcid":"https://orcid.org/0000-0001-5562-5014"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Lieven De Lathauwer","raw_affiliation_strings":["Department of Electrical Engineering, ESAT/- STADIUS, KU Leuven, Leuven, Belgium","Kulak, Kortrijk, Belgium","Group Science, Engineering and Technology, KU Leuven&#x2013"],"raw_orcid":"https://orcid.org/0000-0001-5562-5014","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, ESAT/- STADIUS, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Kulak, Kortrijk, Belgium","institution_ids":[]},{"raw_affiliation_string":"Group Science, Engineering and Technology, KU Leuven&#x2013","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017164422"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.5467,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59832134,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"29","issue":null,"first_page":"937","last_page":"941"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9139999747276306,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.913100004196167,"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/matrix-decomposition","display_name":"Matrix decomposition","score":0.6912338137626648},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6426291465759277},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.6244697570800781},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5973113179206848},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5767030715942383},{"id":"https://openalex.org/keywords/schur-decomposition","display_name":"Schur decomposition","score":0.5432054996490479},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5089426040649414},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4895850121974945},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.47570356726646423},{"id":"https://openalex.org/keywords/tucker-decomposition","display_name":"Tucker decomposition","score":0.46622350811958313},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.46036258339881897},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4577547311782837},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4459456205368042},{"id":"https://openalex.org/keywords/generalized-eigenvector","display_name":"Generalized eigenvector","score":0.4177300035953522},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.4163574278354645},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.4152248501777649},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3683282732963562},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3679218888282776},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3387076258659363},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"Tensor decomposition","score":0.33079054951667786},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2829596996307373},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.2675851583480835},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21318677067756653},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.21306583285331726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1646726429462433},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.10381314158439636},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.10365703701972961}],"concepts":[{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6912338137626648},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6426291465759277},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.6244697570800781},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5973113179206848},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5767030715942383},{"id":"https://openalex.org/C99383703","wikidata":"https://www.wikidata.org/wiki/Q1064218","display_name":"Schur decomposition","level":4,"score":0.5432054996490479},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5089426040649414},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4895850121974945},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47570356726646423},{"id":"https://openalex.org/C42704193","wikidata":"https://www.wikidata.org/wiki/Q7851097","display_name":"Tucker decomposition","level":4,"score":0.46622350811958313},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.46036258339881897},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4577547311782837},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4459456205368042},{"id":"https://openalex.org/C147925508","wikidata":"https://www.wikidata.org/wiki/Q970767","display_name":"Generalized eigenvector","level":5,"score":0.4177300035953522},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.4163574278354645},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.4152248501777649},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3683282732963562},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3679218888282776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3387076258659363},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.33079054951667786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2829596996307373},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.2675851583480835},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21318677067756653},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.21306583285331726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1646726429462433},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.10381314158439636},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.10365703701972961},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2022.3156870","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2022.3156870","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/691336","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/691336","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"Ieee Signal Processing Letters, vol. 29, (937-941)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/691336","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/691336","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"Ieee Signal Processing Letters, vol. 29, (937-941)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1755563775","https://openalex.org/W1974785908","https://openalex.org/W2010802658","https://openalex.org/W2013912476","https://openalex.org/W2027201767","https://openalex.org/W2033154334","https://openalex.org/W2033693394","https://openalex.org/W2057503509","https://openalex.org/W2078789945","https://openalex.org/W2079705627","https://openalex.org/W2101641981","https://openalex.org/W2119412403","https://openalex.org/W2128131274","https://openalex.org/W2160664759","https://openalex.org/W2469230926","https://openalex.org/W2964313686","https://openalex.org/W3102183770","https://openalex.org/W4214731313","https://openalex.org/W4214916906","https://openalex.org/W4229972328","https://openalex.org/W4312258136"],"related_works":["https://openalex.org/W2945356277","https://openalex.org/W2949139067","https://openalex.org/W2089441007","https://openalex.org/W4283821751","https://openalex.org/W3097790858","https://openalex.org/W4312203815","https://openalex.org/W2393920986","https://openalex.org/W2901457990","https://openalex.org/W4363650386","https://openalex.org/W2087995683"],"abstract_inverted_index":{"The":[0,40],"canonical":[1],"decomposition":[2,8,47,80,132,151],"(CPD)":[3],"is":[4,37,76,121,152],"a":[5,11,14,33,48,63,74,84,88,103,130,135,140,149,153,168],"fundamental":[6],"tensor":[7,12,36],"which":[9,82,107,133],"expresses":[10],"as":[13,54,139,167],"sum":[15],"of":[16,32,43,59,65,73,87,95,105,111,137,142,171],"rank":[17,35],"one":[18],"tensors.":[19],"In":[20,98],"stark":[21],"contrast":[22],"to":[23],"the":[24,30,77,92,96,109,112,115],"matrix":[25,85],"case,":[26],"with":[27],"light":[28],"assumptions,":[29],"CPD":[31,44,75],"low":[34],"(essentially)":[38],"unique.":[39],"essential":[41],"uniqueness":[42],"makes":[45],"this":[46,99],"powerful":[49],"tool":[50],"in":[51,119,122],"many":[52],"applications":[53],"it":[55],"allows":[56],"for":[57,70],"extraction":[58],"component":[60],"information":[61],"from":[62],"signal":[64],"interest.":[66],"One":[67],"popular":[68],"algorithm":[69,163],"algebraic":[71],"computation":[72,118],"generalized":[78,93,116,159],"eigenvalue":[79],"(GEVD)":[81],"selects":[83],"subpencil":[86],"tensor,":[89],"then":[90],"computes":[91],"eigenvectors":[94],"pencil.":[97],"article,":[100],"we":[101],"present":[102],"simplification":[104,170],"GEVD":[106,120],"improves":[108],"accuracy":[110],"algorithm.":[113],"Surprisingly,":[114],"eigenvector":[117],"fact":[123],"unnecessary":[124],"and":[125,144],"can":[126,164],"be":[127],"replaced":[128],"by":[129],"QZ":[131,150],"factors":[134],"pair":[136],"matrices":[138],"product":[141],"unitary":[143],"upper":[145],"triangular":[146],"matrices.":[147],"Computing":[148],"standard":[154],"first":[155],"step":[156],"when":[157],"computing":[158],"eigenvectors,":[160],"so":[161],"our":[162],"been":[165],"seen":[166],"direct":[169],"GEVD.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
