{"id":"https://openalex.org/W2732088868","doi":"https://doi.org/10.1137/17m1116672","title":"The Numerical Range is a $(1+\\sqrt{2})$-Spectral Set","display_name":"The Numerical Range is a $(1+\\sqrt{2})$-Spectral Set","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2732088868","doi":"https://doi.org/10.1137/17m1116672","mag":"2732088868"},"language":"en","primary_location":{"id":"doi:10.1137/17m1116672","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1116672","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/A5045416083","display_name":"Michel Crouzeix","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Crouzeix","raw_affiliation_strings":["Institut de Recherche Math\u00e9matique de Rennes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Recherche Math\u00e9matique de Rennes","institution_ids":["https://openalex.org/I4210161663"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071774455","display_name":"C. Palencia","orcid":"https://orcid.org/0000-0003-1823-1395"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"C. Palencia","raw_affiliation_strings":["Laboratorio de Procesado de Imagen [Valladolid]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratorio de Procesado de Imagen [Valladolid]","institution_ids":["https://openalex.org/I108103353"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":19.4871,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.99874832,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"38","issue":"2","first_page":"649","last_page":"655"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9973999857902527,"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/numerical-range","display_name":"Numerical range","score":0.9223594069480896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8819918036460876},{"id":"https://openalex.org/keywords/holomorphic-function","display_name":"Holomorphic function","score":0.7764811515808105},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.632747232913971},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5910751819610596},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4921702742576599},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.4791642725467682},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43233534693717957},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4255332052707672},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3817695379257202},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3736242651939392},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3499528765678406}],"concepts":[{"id":"https://openalex.org/C193060811","wikidata":"https://www.wikidata.org/wiki/Q1579053","display_name":"Numerical range","level":2,"score":0.9223594069480896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8819918036460876},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.7764811515808105},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.632747232913971},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5910751819610596},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4921702742576599},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.4791642725467682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43233534693717957},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4255332052707672},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3817695379257202},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3736242651939392},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3499528765678406},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1116672","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1116672","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:HAL:hal-01455243v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01455243","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 Matrix Analysis and Applications, 2017, 38 (2), pp.649-655. ⟨10.1137/17M1116672⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3597637701","display_name":"Centre de Math\u00e9matiques Henri Lebesgue : fondements, interactions, applications et Formation","funder_award_id":"ANR-11-LABX-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1977960169","https://openalex.org/W1985453997","https://openalex.org/W1990831884","https://openalex.org/W2005916081","https://openalex.org/W2046511598","https://openalex.org/W2066703940","https://openalex.org/W2083039183","https://openalex.org/W2087373438","https://openalex.org/W2258841517","https://openalex.org/W2298037997","https://openalex.org/W2548626409","https://openalex.org/W2962952291","https://openalex.org/W4253628723"],"related_works":["https://openalex.org/W2211201902","https://openalex.org/W3094515845","https://openalex.org/W2982338311","https://openalex.org/W4237698157","https://openalex.org/W4248353673","https://openalex.org/W2295512640","https://openalex.org/W2963148357","https://openalex.org/W2921791553","https://openalex.org/W1758788615","https://openalex.org/W2389165726"],"abstract_inverted_index":{"It":[0],"is":[1,15],"shown":[2],"that":[3],"the":[4,27,30,34],"numerical":[5],"range":[6],"of":[7,29,33,36],"a":[8,12,16],"linear":[9],"operator":[10],"on":[11,26],"Hilbert":[13],"space":[14],"(complete)":[17],"$(1{+}\\sqrt{2})$-spectral":[18],"set.":[19],"The":[20],"proof":[21],"relies,":[22],"among":[23],"other":[24],"things,":[25],"behavior":[28],"Cauchy":[31],"transform":[32],"conjugates":[35],"holomorphic":[37],"functions.":[38]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":32},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":2}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2017-07-14T00:00:00"}