{"id":"https://openalex.org/W2015104712","doi":"https://doi.org/10.1080/00207160903469685","title":"Perturbation analysis of the generalized Sylvester equation and the generalized Lyapunov equation","display_name":"Perturbation analysis of the generalized Sylvester equation and the generalized Lyapunov equation","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2015104712","doi":"https://doi.org/10.1080/00207160903469685","mag":"2015104712"},"language":"en","primary_location":{"id":"doi:10.1080/00207160903469685","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160903469685","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5029270211","display_name":"Yaoping Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I24407930","display_name":"Hunan University of Science and Engineering","ror":"https://ror.org/04ymz0q33","country_code":"CN","type":"education","lineage":["https://openalex.org/I24407930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaoping Tang","raw_affiliation_strings":["a   Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100,  China","Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, China"],"affiliations":[{"raw_affiliation_string":"a   Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100,  China","institution_ids":["https://openalex.org/I24407930"]},{"raw_affiliation_string":"Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, China","institution_ids":["https://openalex.org/I24407930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018729096","display_name":"Liang Bao","orcid":"https://orcid.org/0000-0003-1710-4335"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liang Bao","raw_affiliation_strings":["b   Department of Mathematics , East China University of Science and Technology , Shanghai, 200237,  China","Department of Mathematics , East China University of Science and Technology , Shanghai, 200237, China"],"affiliations":[{"raw_affiliation_string":"b   Department of Mathematics , East China University of Science and Technology , Shanghai, 200237,  China","institution_ids":["https://openalex.org/I143593769"]},{"raw_affiliation_string":"Department of Mathematics , East China University of Science and Technology , Shanghai, 200237, China","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053003412","display_name":"Yiqin Lin","orcid":"https://orcid.org/0000-0003-2813-3860"},"institutions":[{"id":"https://openalex.org/I24407930","display_name":"Hunan University of Science and Engineering","ror":"https://ror.org/04ymz0q33","country_code":"CN","type":"education","lineage":["https://openalex.org/I24407930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiqin Lin","raw_affiliation_strings":["a   Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100,  China","Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, China"],"affiliations":[{"raw_affiliation_string":"a   Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100,  China","institution_ids":["https://openalex.org/I24407930"]},{"raw_affiliation_string":"Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, China","institution_ids":["https://openalex.org/I24407930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018729096"],"corresponding_institution_ids":["https://openalex.org/I143593769"],"apc_list":null,"apc_paid":null,"fwci":0.4915,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64805375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"88","issue":"2","first_page":"408","last_page":"420"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"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":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8487534523010254},{"id":"https://openalex.org/keywords/sylvester-equation","display_name":"Sylvester equation","score":0.8169834613800049},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6178189516067505},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5650181770324707},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4656691551208496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4080420136451721},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.391845166683197},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09146630764007568},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06390306353569031}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8487534523010254},{"id":"https://openalex.org/C100468782","wikidata":"https://www.wikidata.org/wiki/Q3730848","display_name":"Sylvester equation","level":3,"score":0.8169834613800049},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6178189516067505},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5650181770324707},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4656691551208496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4080420136451721},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.391845166683197},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09146630764007568},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06390306353569031},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160903469685","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160903469685","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1512415169","https://openalex.org/W1530239534","https://openalex.org/W1551480811","https://openalex.org/W1941583664","https://openalex.org/W1988467199","https://openalex.org/W2000630868","https://openalex.org/W2040608867","https://openalex.org/W2044431299","https://openalex.org/W2045973172","https://openalex.org/W2054390548","https://openalex.org/W2054689585","https://openalex.org/W2078488968","https://openalex.org/W2081128548","https://openalex.org/W2081157748","https://openalex.org/W2088748973","https://openalex.org/W2123505857"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W1977987201","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W2106169668","https://openalex.org/W2534107666"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"devoted":[3],"to":[4],"the":[5,9,14],"perturbation":[6],"analysis":[7],"for":[8,31],"generalized":[10,15],"Sylvester":[11],"equation":[12],"and":[13,21,27],"Lyapunov":[16],"equation.":[17],"The":[18,36],"explicit":[19],"expressions":[20],"upper":[22],"bounds":[23],"of":[24],"normwise,":[25],"mixed":[26],"componentwise":[28],"condition":[29],"numbers":[30],"these":[32],"equations":[33],"are":[34,38],"presented.":[35],"results":[37],"illustrated":[39],"by":[40],"numerical":[41],"examples.":[42]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
