{"id":"https://openalex.org/W1979468491","doi":"https://doi.org/10.1137/s0895479893246005","title":"Bounding the Subspaces from Rank Revealing Two-Sided Orthogonal Decompositions","display_name":"Bounding the Subspaces from Rank Revealing Two-Sided Orthogonal Decompositions","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W1979468491","doi":"https://doi.org/10.1137/s0895479893246005","mag":"1979468491"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479893246005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893246005","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/A5056924173","display_name":"Ricardo D. Fierro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ricardo D. Fierro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074956539","display_name":"James R. Bunch","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James R. Bunch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.95,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.97592068,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"3","first_page":"743","last_page":"759"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/T13487","display_name":"Statistical and numerical algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/singular-value-decomposition","display_name":"Singular value decomposition","score":0.859653115272522},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8363958597183228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6926115155220032},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6261634826660156},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.6233446002006531},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5791459083557129},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5264604687690735},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4737447202205658},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47272270917892456},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.465547651052475},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.4651392996311188},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4376845359802246},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.41064733266830444},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4069961607456207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.340977281332016},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12396511435508728},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11404150724411011},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.09724056720733643},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09422650933265686},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08838838338851929}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.859653115272522},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8363958597183228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6926115155220032},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6261634826660156},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.6233446002006531},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5791459083557129},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5264604687690735},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4737447202205658},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47272270917892456},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.465547651052475},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.4651392996311188},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4376845359802246},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.41064733266830444},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4069961607456207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.340977281332016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12396511435508728},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11404150724411011},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.09724056720733643},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09422650933265686},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08838838338851929},{"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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479893246005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893246005","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1906681256","https://openalex.org/W1974986527","https://openalex.org/W1982143352","https://openalex.org/W2007871293","https://openalex.org/W2008205484","https://openalex.org/W2009193081","https://openalex.org/W2014042806","https://openalex.org/W2020727186","https://openalex.org/W2023054423","https://openalex.org/W2035885121","https://openalex.org/W2040528593","https://openalex.org/W2046164006","https://openalex.org/W2064667796","https://openalex.org/W2092414156","https://openalex.org/W2105292630","https://openalex.org/W2128131274","https://openalex.org/W2141244461","https://openalex.org/W2166036437","https://openalex.org/W2170238574","https://openalex.org/W2333836441","https://openalex.org/W4206428854"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W3046517157","https://openalex.org/W4382583540","https://openalex.org/W2002598339","https://openalex.org/W2150953077","https://openalex.org/W2148568324","https://openalex.org/W2059421710","https://openalex.org/W2770973630","https://openalex.org/W2274293306","https://openalex.org/W2140805692"],"abstract_inverted_index":{"The":[0,29],"singular":[1],"value":[2],"decomposition":[3,34],"(SVD)":[4],"is":[5,20,150],"a":[6,74,117],"widely":[7],"used":[8],"computational":[9],"tool":[10],"in":[11,15,145,164],"various":[12],"applications.":[13],"However,":[14],"some":[16],"applications":[17,154],"the":[18,36,48,79,82,94,97,101,108,111,134,137,143,156],"SVD":[19,135],"viewed":[21],"as":[22,163],"computationally":[23],"demanding":[24],"or":[25,103,167],"difficult":[26],"to":[27,133],"update.":[28],"rank":[30,50],"revealing":[31],"QR":[32],"(RRQR)":[33],"and":[35,40,58,114],"recently":[37],"proposed":[38],"URV":[39,102],"ULV":[41,104],"decompositions":[42,127],"are":[43],"promising":[44],"alternatives":[45,132],"for":[46,77,153],"determining":[47],"numerical":[49,62],"k":[51],"of":[52,81,96,110],"an":[53,146],"$m":[54],"\\times":[55],"n$":[56],"matrix":[57],"approximating":[59],"its":[60],"fundamental":[61],"subspaces":[63,83,98],"whenever":[64],"$k":[65],"\\approx":[66],"\\min":[67],"(m,n)$.":[68],"In":[69,89],"this":[70],"paper":[71],"we":[72,91,123,141],"prove":[73],"posteriori":[75],"bounds":[76],"assessing":[78],"quality":[80,95,109],"obtained":[84,99],"by":[85,100],"two-sided":[86],"orthogonal":[87],"decompositions.":[88],"particular,":[90],"show":[92],"that":[93,125],"algorithm":[105],"depends":[106],"on":[107,116],"condition":[112],"estimator":[113],"not":[115],"gap":[118],"condition.":[119],"From":[120],"our":[121],"analysis":[122],"conclude":[124],"these":[126],"may":[128],"be":[129,160],"more":[130],"accurate":[131],"than":[136],"RRQR":[138],"decomposition.":[139],"Finally,":[140],"implement":[142],"algorithms":[144],"adaptive":[147],"manner,":[148],"which":[149],"particularly":[151],"useful":[152],"where":[155],"\u201cnoise\u201d":[157],"subspace":[158],"must":[159],"computed,":[161],"such":[162],"signal":[165],"processing":[166],"total":[168],"least":[169],"squares.":[170]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}