{"id":"https://openalex.org/W2053039356","doi":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<1::aid-nla121>3.0.co;2-x","title":"A note on the normwise perturbation theory for the regular generalized eigenproblem","display_name":"A note on the normwise perturbation theory for the regular generalized eigenproblem","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2053039356","doi":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<1::aid-nla121>3.0.co;2-x","mag":"2053039356"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199801/02)5:1<1::aid-nla121>3.0.co;2-x","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<1::aid-nla121>3.0.co;2-x","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5073044597","display_name":"Val\u00e9rie Frayss\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Val\u00e9rie Frayss\u00e9","raw_affiliation_strings":["CERFACS, 42 av. Coriolis, 31057 Toulouse Cedex, France"],"affiliations":[{"raw_affiliation_string":"CERFACS, 42 av. Coriolis, 31057 Toulouse Cedex, France","institution_ids":["https://openalex.org/I4210106946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031207213","display_name":"Vincent Toumazou","orcid":null},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Toumazou","raw_affiliation_strings":["CERFACS, 42 av. Coriolis, 31057 Toulouse Cedex, France"],"affiliations":[{"raw_affiliation_string":"CERFACS, 42 av. Coriolis, 31057 Toulouse Cedex, France","institution_ids":["https://openalex.org/I4210106946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073044597"],"corresponding_institution_ids":["https://openalex.org/I4210106946"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":5.0845,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.95781508,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8481956720352173},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7481632828712463},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5999553799629211},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5314924716949463},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49451562762260437},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.4153839647769928}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8481956720352173},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7481632828712463},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5999553799629211},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5314924716949463},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49451562762260437},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.4153839647769928},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199801/02)5:1<1::aid-nla121>3.0.co;2-x","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<1::aid-nla121>3.0.co;2-x","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.37.5350","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.5350","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cerfacs.fr/algor/reports/1996/TR_PA_96_18.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W401710980","https://openalex.org/W658559791","https://openalex.org/W1514113870","https://openalex.org/W1985910458","https://openalex.org/W2006411943","https://openalex.org/W2008256634","https://openalex.org/W2011906094","https://openalex.org/W4285019923","https://openalex.org/W6613795344","https://openalex.org/W6621858757"],"related_works":["https://openalex.org/W2062626603","https://openalex.org/W2165749285","https://openalex.org/W2474979212","https://openalex.org/W2562455930","https://openalex.org/W2001036795","https://openalex.org/W2154748900","https://openalex.org/W3093811938","https://openalex.org/W2062690431","https://openalex.org/W2088932963","https://openalex.org/W2893622182"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5,20,40,46],"normwise":[6],"perturbation":[7],"theory":[8],"for":[9,45],"the":[10,28,32,56],"regular":[11],"generalized":[12],"eigenproblem":[13],"Ax":[14],"=":[15],"\u03bbBx,":[16],"when":[17],"\u03bb":[18],"is":[19,72],"semi-simple":[21],"and":[22,39,59],"finite":[23],"eigenvalue,":[24],"which":[25],"departs":[26],"from":[27],"classical":[29],"analysis":[30],"with":[31,68],"chordal":[33],"norm":[34],"[9].":[35],"A":[36,58],"backward":[37,65],"error":[38,66],"condition":[41],"number":[42],"are":[43],"derived":[44],"choice":[47],"of":[48,63],"flexible":[49],"measure":[50],"to":[51],"represent":[52],"independent":[53],"perturbations":[54],"in":[55],"matrices":[57],"B.":[60],"The":[61],"concept":[62],"optimal":[64],"associated":[67],"an":[69],"eigenvalue":[70],"only":[71],"also":[73],"discussed.":[74],"\u00a9":[75],"1998":[76],"John":[77],"Wiley":[78],"&":[79],"Sons,":[80],"Ltd.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}