{"id":"https://openalex.org/W2548626409","doi":"https://doi.org/10.1007/s10107-016-1083-6","title":"Variational analysis of the Crouzeix ratio","display_name":"Variational analysis of the Crouzeix ratio","publication_year":2016,"publication_date":"2016-11-02","ids":{"openalex":"https://openalex.org/W2548626409","doi":"https://doi.org/10.1007/s10107-016-1083-6","mag":"2548626409"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-016-1083-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-016-1083-6","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","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/A5019550551","display_name":"Anne Greenbaum","orcid":"https://orcid.org/0000-0002-3783-3466"},"institutions":[{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anne Greenbaum","raw_affiliation_strings":["Department of Applied Mathematics, University of Washington, Seattle, WA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I4210138199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081400874","display_name":"Adrian S. Lewis","orcid":"https://orcid.org/0000-0002-1785-1106"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adrian S. Lewis","raw_affiliation_strings":["Department of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069099932","display_name":"Michael L. Overton","orcid":"https://orcid.org/0000-0002-6563-6371"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael L. Overton","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, NY, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069099932"],"corresponding_institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":1.631,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86126246,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"164","issue":"1-2","first_page":"229","last_page":"243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9994000196456909,"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":0.8913552761077881},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6275937557220459},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5836154818534851},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5272416472434998},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4978933334350586},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4932541251182556},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4594271183013916},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4280540943145752},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40669769048690796},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26760774850845337}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8913552761077881},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6275937557220459},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5836154818534851},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5272416472434998},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4978933334350586},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4932541251182556},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4594271183013916},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4280540943145752},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40669769048690796},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26760774850845337},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-016-1083-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-016-1083-6","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5037380382","display_name":null,"funder_award_id":"DMS-1210886","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5618045529","display_name":null,"funder_award_id":"DMS-1208338","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5991450763","display_name":null,"funder_award_id":"DMS-1317205","funder_id":"https://openalex.org/F4320309856","funder_display_name":"National Youth Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309856","display_name":"National Youth Science Foundation","ror":"https://ror.org/054yz2f06"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1551360398","https://openalex.org/W2000844563","https://openalex.org/W2005216560","https://openalex.org/W2005916081","https://openalex.org/W2021525163","https://openalex.org/W2029213856","https://openalex.org/W2042608503","https://openalex.org/W2044615981","https://openalex.org/W2046011269","https://openalex.org/W2046511598","https://openalex.org/W2079055561","https://openalex.org/W2083039183","https://openalex.org/W2087373438","https://openalex.org/W2258841517","https://openalex.org/W2611283298","https://openalex.org/W2777260113","https://openalex.org/W3157341860","https://openalex.org/W4249513058","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W1973978937","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W4286909116","https://openalex.org/W4292635168"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
