{"id":"https://openalex.org/W1994157509","doi":"https://doi.org/10.1137/s0895479804439791","title":"A New Approach to Generalized Singular Value Decomposition","display_name":"A New Approach to Generalized Singular Value Decomposition","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1994157509","doi":"https://doi.org/10.1137/s0895479804439791","mag":"1994157509"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479804439791","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479804439791","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/A5002855648","display_name":"Shmuel Friedland","orcid":"https://orcid.org/0000-0002-0423-5005"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shmuel Friedland","raw_affiliation_strings":["University of Illinois at Chicago"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002855648"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":0.3379,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.60013529,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"2","first_page":"434","last_page":"444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.982699990272522,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.872089147567749},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8474438786506653},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6881639957427979},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.6770201921463013},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4845956563949585},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.47900933027267456},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.45587366819381714},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41007113456726074},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3409573435783386},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2858915328979492},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.20419928431510925},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13802176713943481}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.872089147567749},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8474438786506653},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6881639957427979},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.6770201921463013},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4845956563949585},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.47900933027267456},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.45587366819381714},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41007113456726074},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3409573435783386},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2858915328979492},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.20419928431510925},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13802176713943481},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479804439791","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479804439791","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1962116664","https://openalex.org/W1985852691","https://openalex.org/W2112440119","https://openalex.org/W2129256542","https://openalex.org/W2148541040","https://openalex.org/W2162302435","https://openalex.org/W2372058311","https://openalex.org/W2610857016","https://openalex.org/W2798909945","https://openalex.org/W4301773902"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W2147072251","https://openalex.org/W2148568324","https://openalex.org/W1607100495","https://openalex.org/W4386721910","https://openalex.org/W4378770618","https://openalex.org/W2164147222","https://openalex.org/W2038393145","https://openalex.org/W2594811212"],"abstract_inverted_index":{"We":[0,21],"propose":[1],"a":[2,40],"new":[3],"algorithm":[4,29],"to":[5,30,42],"find":[6],"the":[7,16,25,33,36],"generalized":[8],"singular":[9],"value":[10],"decompositions":[11],"of":[12,19,27,35],"two":[13],"matrices":[14,37],"with":[15],"same":[17],"number":[18],"columns.":[20],"discuss":[22],"in":[23,32],"detail":[24],"sensitivity":[26],"our":[28],"errors":[31],"entries":[34],"and":[38],"suggest":[39],"way":[41],"suppress":[43],"this":[44],"sensitivity.":[45]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}
