{"id":"https://openalex.org/W2061242746","doi":"https://doi.org/10.1137/s0363012903432365","title":"Robust Root-Clustering of a Matrix in Intersections or Unions of Regions","display_name":"Robust Root-Clustering of a Matrix in Intersections or Unions of Regions","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2061242746","doi":"https://doi.org/10.1137/s0363012903432365","mag":"2061242746"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012903432365","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012903432365","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5033272751","display_name":"Olivier Bachelier","orcid":"https://orcid.org/0000-0002-1655-891X"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Bachelier","raw_affiliation_strings":["LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)","institution_ids":["https://openalex.org/I4210116740"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074893139","display_name":"Didier Henrion","orcid":"https://orcid.org/0000-0001-6735-7715"},"institutions":[{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I190497903","https://openalex.org/I193033237","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210152422","https://openalex.org/I4210159245","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ","FR"],"is_corresponding":false,"raw_author_name":"Didier Henrion","raw_affiliation_strings":["LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)","CTU - Czech Technical University in Prague (\u010cesk\u00e9 vysok\u00e9 u\u010den\u00ed technick\u00e9 v Praze Zikova 1903/4 166 36 Praha 6 \u010cesk\u00e1 republika - Czech Republic)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)","institution_ids":["https://openalex.org/I190497903"]},{"raw_affiliation_string":"CTU - Czech Technical University in Prague (\u010cesk\u00e9 vysok\u00e9 u\u010den\u00ed technick\u00e9 v Praze Zikova 1903/4 166 36 Praha 6 \u010cesk\u00e1 republika - Czech Republic)","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008497394","display_name":"B. Pradin","orcid":null},"institutions":[{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I190497903","https://openalex.org/I193033237","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210152422","https://openalex.org/I4210159245","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bernard Pradin","raw_affiliation_strings":["LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)","institution_ids":["https://openalex.org/I190497903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012039416","display_name":"Driss Mehdi","orcid":"https://orcid.org/0000-0002-0045-7364"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Driss Mehdi","raw_affiliation_strings":["LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)","institution_ids":["https://openalex.org/I4210116740"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4861,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.91930869,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"43","issue":"3","first_page":"1078","last_page":"1093"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9894000291824341,"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/T11236","display_name":"Control Systems and Identification","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8529341816902161},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7168521881103516},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6857735514640808},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6239733695983887},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5894864797592163},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5377059578895569},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.49553072452545166},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4561883211135864},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.44543200731277466},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4286411702632904},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33360499143600464},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.325022429227829},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2163623869419098},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1297490894794464},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10356250405311584},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10156494379043579},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10141885280609131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09136056900024414}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8529341816902161},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7168521881103516},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6857735514640808},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6239733695983887},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5894864797592163},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5377059578895569},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.49553072452545166},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4561883211135864},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.44543200731277466},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4286411702632904},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33360499143600464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.325022429227829},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2163623869419098},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1297490894794464},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10356250405311584},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10156494379043579},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10141885280609131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09136056900024414},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0363012903432365","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012903432365","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03360883v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03360883","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2004, 43 (3), pp.1078--1093. &#x27E8;10.1137/S0363012903432365&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W816406765","https://openalex.org/W1514857503","https://openalex.org/W1525469484","https://openalex.org/W1547135986","https://openalex.org/W1575783483","https://openalex.org/W1966103588","https://openalex.org/W1966397236","https://openalex.org/W1972848510","https://openalex.org/W1992363721","https://openalex.org/W1994873143","https://openalex.org/W2002357820","https://openalex.org/W2034539682","https://openalex.org/W2036767392","https://openalex.org/W2039867272","https://openalex.org/W2048187422","https://openalex.org/W2050649877","https://openalex.org/W2051114549","https://openalex.org/W2054155441","https://openalex.org/W2055319245","https://openalex.org/W2059507126","https://openalex.org/W2075291379","https://openalex.org/W2077418568","https://openalex.org/W2080153087","https://openalex.org/W2086264563","https://openalex.org/W2109090100","https://openalex.org/W2110683518","https://openalex.org/W2125190651","https://openalex.org/W2178909929","https://openalex.org/W2333053474","https://openalex.org/W2476002252","https://openalex.org/W4243620103"],"related_works":["https://openalex.org/W1502458949","https://openalex.org/W2323830966","https://openalex.org/W2362838148","https://openalex.org/W188032563","https://openalex.org/W2359279826","https://openalex.org/W2085581092","https://openalex.org/W2361901126","https://openalex.org/W2387523877","https://openalex.org/W3210250802","https://openalex.org/W2360232153"],"abstract_inverted_index":{"International":[0],"audience":[1]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
