{"id":"https://openalex.org/W2163255469","doi":"https://doi.org/10.1137/s0895479893261340","title":"A Schur Method for Low-Rank Matrix Approximation","display_name":"A Schur Method for Low-Rank Matrix Approximation","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2163255469","doi":"https://doi.org/10.1137/s0895479893261340","mag":"2163255469"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479893261340","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893261340","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/A5011134257","display_name":"A. van Veen","orcid":"https://orcid.org/0000-0003-4249-585X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alle-Jan van der Veen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011134257"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.773,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.90267078,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"17","issue":"1","first_page":"139","last_page":"160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9980000257492065,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8864986896514893},{"id":"https://openalex.org/keywords/schur-decomposition","display_name":"Schur decomposition","score":0.8661871552467346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8092460632324219},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.7511892914772034},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6007800102233887},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5884316563606262},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.587407648563385},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.5786174535751343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.525205671787262},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5162270069122314},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.5064162015914917},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.48322996497154236},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4636268615722656},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3563530445098877},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30685049295425415},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2581367492675781},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.19625484943389893}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8864986896514893},{"id":"https://openalex.org/C99383703","wikidata":"https://www.wikidata.org/wiki/Q1064218","display_name":"Schur decomposition","level":4,"score":0.8661871552467346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8092460632324219},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.7511892914772034},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6007800102233887},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5884316563606262},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.587407648563385},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.5786174535751343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.525205671787262},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5162270069122314},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.5064162015914917},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.48322996497154236},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4636268615722656},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3563530445098877},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30685049295425415},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2581367492675781},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.19625484943389893},{"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/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/s0895479893261340","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893261340","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:CiteSeerX.psu:10.1.1.35.8197","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.8197","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://cas.et.tudelft.nl/pub/allejan-docs/spie94a.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.55.1785","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.1785","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://cas.et.tudelft.nl/pub/allejan-docs/schur93.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.74.5278","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.74.5278","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ens.ewi.tudelft.nl/pubs/schur93.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.673","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.673","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ens.ewi.tudelft.nl/pubs/spie94a.pdf","raw_type":"text"},{"id":"pmh:oai:tudelft.nl:uuid:18f07e99-20b2-4814-bbcc-fe9e35c566d5","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:18f07e99-20b2-4814-bbcc-fe9e35c566d5","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321012","display_name":"Technische Universiteit Delft","ror":"https://ror.org/02e2c7k09"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W620523544","https://openalex.org/W1504633463","https://openalex.org/W1568619395","https://openalex.org/W1599533721","https://openalex.org/W1967332578","https://openalex.org/W1974336305","https://openalex.org/W1984714339","https://openalex.org/W2005198822","https://openalex.org/W2007338024","https://openalex.org/W2007871293","https://openalex.org/W2008205484","https://openalex.org/W2009193081","https://openalex.org/W2013501249","https://openalex.org/W2015071882","https://openalex.org/W2019433012","https://openalex.org/W2021344000","https://openalex.org/W2028213769","https://openalex.org/W2033332370","https://openalex.org/W2035885121","https://openalex.org/W2038610163","https://openalex.org/W2045785683","https://openalex.org/W2056480844","https://openalex.org/W2057682788","https://openalex.org/W2062481674","https://openalex.org/W2064468023","https://openalex.org/W2065405327","https://openalex.org/W2070013817","https://openalex.org/W2088028877","https://openalex.org/W2105111377","https://openalex.org/W2115862150","https://openalex.org/W2130739159","https://openalex.org/W2141244461","https://openalex.org/W2156979967","https://openalex.org/W2163971036","https://openalex.org/W2172190709","https://openalex.org/W2798909945","https://openalex.org/W3046452920","https://openalex.org/W4250038851","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1975201729","https://openalex.org/W2064598248","https://openalex.org/W3092306907","https://openalex.org/W2074771309","https://openalex.org/W1985400098","https://openalex.org/W1510582995","https://openalex.org/W4221157149","https://openalex.org/W1986380039","https://openalex.org/W1584507820","https://openalex.org/W2146459776"],"abstract_inverted_index":{"The":[0,68,77],"usual":[1],"way":[2],"to":[3,13,33,93,121],"compute":[4,34],"a":[5,9,27,39,87,94,124],"low-rank":[6,36],"approximant":[7],"of":[8,70,79,101,105,127],"matrix":[10,41],"H":[11,42,60],"is":[12,21],"take":[14],"its":[15],"truncated":[16,74],"SVD.":[17],"However,":[18],"the":[19,73,80,102,106],"SVD":[20,75],"computationally":[22],"expensive.":[23],"This":[24,108],"paper":[25],"describes":[26],"much":[28,88],"simpler":[29],"generalized":[30],"Schur-type":[31],"algorithm":[32,82],"similar":[35],"approximants.":[37,107],"For":[38],"given":[40],"which":[43],"has":[44,63,86],"d":[45,55],"singular":[46],"values":[47],"larger":[48],"than":[49,66],"\u03b5,":[50],"we":[51],"find":[52],"all":[53],"rank":[54],"approximants":[56,71],"\u02c6H":[57,62],"such":[58],"that":[59,84],"\u2212":[61],"2-norm":[64],"less":[65],"\u03b5.":[67],"set":[69],"includes":[72],"approximation.":[76],"advantages":[78],"Schur":[81],"are":[83],"it":[85],"lower":[89],"computational":[90],"complexity":[91],"(similar":[92],"QR":[95],"factorization),":[96],"and":[97,114],"directly":[98],"produces":[99],"estimates":[100],"column":[103,109],"space":[104,110],"can":[111],"be":[112],"updated":[113],"downdated":[115],"in":[116],"an":[117],"on-line":[118],"scheme,":[119],"amenable":[120],"implementation":[122],"on":[123],"parallel":[125],"array":[126],"processors.":[128]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}