{"id":"https://openalex.org/W1974986527","doi":"https://doi.org/10.1137/s0895479894264491","title":"Perturbation Analysis for Two-Sided (or Complete) Orthogonal Decompositions","display_name":"Perturbation Analysis for Two-Sided (or Complete) Orthogonal Decompositions","publication_year":1996,"publication_date":"1996-04-01","ids":{"openalex":"https://openalex.org/W1974986527","doi":"https://doi.org/10.1137/s0895479894264491","mag":"1974986527"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479894264491","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894264491","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":true,"raw_author_name":"Ricardo D. Fierro","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056924173"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2798,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.90939304,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"2","first_page":"383","last_page":"400"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9986000061035156,"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":0.9986000061035156,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8557708263397217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8505591154098511},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7880146503448486},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5786430239677429},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5737495422363281},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5445948839187622},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4929203987121582},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4701046347618103},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.43006765842437744},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4251770079135895},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4191421866416931},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4190395474433899},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3326416313648224},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31264275312423706},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3082878589630127},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16621321439743042},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12849777936935425},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08408501744270325},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06934148073196411}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8557708263397217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8505591154098511},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7880146503448486},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5786430239677429},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5737495422363281},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5445948839187622},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4929203987121582},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4701046347618103},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.43006765842437744},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4251770079135895},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4191421866416931},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4190395474433899},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3326416313648224},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31264275312423706},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3082878589630127},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16621321439743042},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12849777936935425},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08408501744270325},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06934148073196411},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479894264491","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894264491","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":[{"id":"https://openalex.org/F4320332603","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1979468491","https://openalex.org/W1982143352","https://openalex.org/W2009867667","https://openalex.org/W2023054423","https://openalex.org/W2028510080","https://openalex.org/W2040528593","https://openalex.org/W2046164006","https://openalex.org/W2064667796","https://openalex.org/W2064980127","https://openalex.org/W2066043610","https://openalex.org/W2067048653","https://openalex.org/W2141244461","https://openalex.org/W2150200785","https://openalex.org/W2170200062"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W1607100495","https://openalex.org/W1990844505","https://openalex.org/W2148568324","https://openalex.org/W4386721910","https://openalex.org/W4378770618","https://openalex.org/W2098709175","https://openalex.org/W4297563640","https://openalex.org/W2951380309"],"abstract_inverted_index":{"Two-sided":[0],"(or":[1],"complete)":[2],"orthogonal":[3,45],"decompositions":[4],"are":[5,57,78],"good":[6,18],"alternatives":[7],"to":[8,20,62,83,94,125],"the":[9,21,38,55,68,71,75,84,87,92,95,102,109,114,137],"singular":[10,65,132],"value":[11],"decomposition":[12,46,103],"(SVD)":[13],"because":[14],"they":[15],"can":[16,122],"yield":[17],"approximations":[19],"fundamental":[22],"subspaces":[23,39,56,133],"associated":[24,40],"with":[25,41,81],"a":[26,42,48],"numerically":[27,49],"rank-deficient":[28,50],"matrix.":[29,51],"In":[30],"this":[31],"paper":[32],"we":[33],"derive":[34],"perturbation":[35,106,129],"bounds":[36,130],"for":[37,108,131],"general":[43],"two-sided":[44],"of":[47,70,74,86,113],"The":[52,119],"results":[53,121],"imply":[54],"only":[58],"slightly":[59],"more":[60],"sensitive":[61],"perturbations":[63],"than":[64],"subspaces,":[66],"provided":[67],"norm":[69,111],"off-diagonal":[72],"blocks":[73],"middle":[76],"matrices":[77],"sufficiently":[79],"small":[80],"respect":[82],"size":[85],"perturbation.":[88],"We":[89],"consider":[90],"regularizing":[91],"solution":[93,112],"ill-conditioned":[96],"least":[97,116,139],"squares":[98,117,140],"problem":[99],"by":[100],"truncating":[101],"and":[104],"present":[105],"theory":[107],"minimum":[110],"resulting":[115],"problem.":[118],"main":[120],"be":[123],"specialized":[124],"well":[126,135],"known":[127],"SVD-based":[128],"as":[134,136],"truncated":[138],"solution.":[141]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
