{"id":"https://openalex.org/W2005393749","doi":"https://doi.org/10.1137/060648969","title":"Combined Perturbation Bounds: I. Eigensystems and Singular Value Decompositions","display_name":"Combined Perturbation Bounds: I. Eigensystems and Singular Value Decompositions","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2005393749","doi":"https://doi.org/10.1137/060648969","mag":"2005393749"},"language":"en","primary_location":{"id":"doi:10.1137/060648969","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060648969","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":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/combined-perturbation-bounds-i-eigensystems-and-singular-value-de","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100320302","display_name":"Wen Li","orcid":"https://orcid.org/0000-0002-6695-4988"},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wen Li","raw_affiliation_strings":["SOUTH CHINA NORMAL UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SOUTH CHINA NORMAL UNIVERSITY","institution_ids":["https://openalex.org/I187400657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014226512","display_name":"Weiwei Sun","orcid":"https://orcid.org/0000-0002-2079-4480"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Weiwei Sun","raw_affiliation_strings":["City University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100320302"],"corresponding_institution_ids":["https://openalex.org/I187400657"],"apc_list":null,"apc_paid":null,"fwci":1.4975,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81829856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"29","issue":"2","first_page":"643","last_page":"655"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9952999949455261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8085179328918457},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8042442798614502},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7954807281494141},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.7647480368614197},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6854647994041443},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6022118926048279},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5557528734207153},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4317271411418915},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.358473002910614},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34560656547546387},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27243572473526},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16707384586334229},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0894995629787445}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8085179328918457},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8042442798614502},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7954807281494141},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7647480368614197},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6854647994041443},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6022118926048279},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5557528734207153},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4317271411418915},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.358473002910614},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34560656547546387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27243572473526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16707384586334229},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0894995629787445}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060648969","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060648969","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"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/combined-perturbation-bounds-i-eigensystems-and-singular-value-de","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:pure.atira.dk:publications/2388a295-3cf9-48df-a011-98b884c5630e","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/2388a295-3cf9-48df-a011-98b884c5630e","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Li, W & Sun, W 2007, 'Combined perturbation bounds : I. Eigensystems and singular value decompositions', SIAM Journal on Matrix Analysis and Applications, vol. 29, no. 2, pp. 643-655. https://doi.org/10.1137/060648969","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/combined-perturbation-bounds-i-eigensystems-and-singular-value-de","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W658559791","https://openalex.org/W1966030791","https://openalex.org/W1966809927","https://openalex.org/W1970377488","https://openalex.org/W1971398013","https://openalex.org/W2018110135","https://openalex.org/W2046164006","https://openalex.org/W2064549639","https://openalex.org/W2068094562","https://openalex.org/W2075334209","https://openalex.org/W2092204459","https://openalex.org/W2099781564","https://openalex.org/W2107002547","https://openalex.org/W3150353689","https://openalex.org/W4252388665"],"related_works":["https://openalex.org/W2921006359","https://openalex.org/W1503817672","https://openalex.org/W2141080975","https://openalex.org/W2038812594","https://openalex.org/W1996057986","https://openalex.org/W3148709143","https://openalex.org/W2740187182","https://openalex.org/W771802720","https://openalex.org/W2802142240","https://openalex.org/W2163229019"],"abstract_inverted_index":{"In":[0,78],"this":[1],"paper":[2],"we":[3],"present":[4],"some":[5],"new":[6],"combined":[7,80,88],"perturbation":[8,81,89],"bounds":[9,82,90],"of":[10,46,64],"eigenvalues":[11,45,55],"and":[12,48,74,87],"eigensubspaces":[13],"for":[14,61,83],"a":[15],"Hermitian":[16],"matrix":[17],"H,":[18],"particularly":[19],"in":[20,91],"an":[21],"asymptotic":[22],"sense,":[23],"$\\delta":[24],"_{12}^{2}\\Vert":[25],"\\sin":[26],"\\Theta":[27],"(U_{1},\\widetilde{U}_{1})\\Vert":[28],"_{F}^{2}+\\sum_{i=1}^{r}(\\lambda":[29],"_{i}-\\widetilde{\\lambda":[30],"}_{i})^{2}":[31],"\\le":[32],"\\Vert":[33],"\\Delta":[34,37],"HU_{1}\\Vert":[35,38],"_{F}^{2}+O(\\Vert":[36],"_{F}^{4})$,":[39],"where":[40],"$\\lambda":[41,56],"_{i}$":[42],"denotes":[43],"the":[44,50,54,70,75],"H":[47],"$U_{1}$":[49],"eigensubspace":[51],"corresponding":[52],"to":[53,69],"_{i}$,":[57],"$i=1,2,\\ldots,r$.":[58],"The":[59],"bound":[60],"each":[62],"factor":[63],"eigensystems":[65],"is":[66],"optimal":[67],"due":[68],"${\\rm{sin}}\\Theta":[71],"$":[72],"theorem":[73],"Hoffman\u2013Wielandt":[76],"theorem.":[77],"addition,":[79],"singular":[84],"value":[85],"decompositions":[86],"some,":[92],"more":[93],"general,":[94],"measures":[95],"are":[96],"also":[97],"obtained.":[98]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-27T08:22:11.395708","created_date":"2025-10-10T00:00:00"}
