{"id":"https://openalex.org/W1993722858","doi":"https://doi.org/10.1007/s10817-012-9256-3","title":"Formalization of Bernstein Polynomials and Applications to Global Optimization","display_name":"Formalization of Bernstein Polynomials and Applications to Global Optimization","publication_year":2012,"publication_date":"2012-07-18","ids":{"openalex":"https://openalex.org/W1993722858","doi":"https://doi.org/10.1007/s10817-012-9256-3","mag":"1993722858"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-012-9256-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-012-9256-3","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"Journal of Automated Reasoning","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/A5016058241","display_name":"C\u00e9sar Mu\u00f1oz","orcid":"https://orcid.org/0000-0003-3579-8254"},"institutions":[{"id":"https://openalex.org/I1319063186","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C\u00e9sar Mu\u00f1oz","raw_affiliation_strings":["NASA Langley Research Center, Hampton, VA, 23681, USA","NASA Langley Research Center, Hampton, USA 23681#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NASA Langley Research Center, Hampton, VA, 23681, USA","institution_ids":["https://openalex.org/I1319063186"]},{"raw_affiliation_string":"NASA Langley Research Center, Hampton, USA 23681#TAB#","institution_ids":["https://openalex.org/I1319063186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000166506","display_name":"Anthony Narkawicz","orcid":null},"institutions":[{"id":"https://openalex.org/I1319063186","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony Narkawicz","raw_affiliation_strings":["NASA Langley Research Center, Hampton, VA, 23681, USA","NASA Langley Research Center, Hampton, USA 23681#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NASA Langley Research Center, Hampton, VA, 23681, USA","institution_ids":["https://openalex.org/I1319063186"]},{"raw_affiliation_string":"NASA Langley Research Center, Hampton, USA 23681#TAB#","institution_ids":["https://openalex.org/I1319063186"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016058241"],"corresponding_institution_ids":["https://openalex.org/I1319063186"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":13.5457,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.99262654,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"51","issue":"2","first_page":"151","last_page":"196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","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/T11435","display_name":"Polynomial and algebraic computation","score":0.9979000091552734,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9973000288009644,"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/representation","display_name":"Representation (politics)","score":0.6737675666809082},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.6329585909843445},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5500279664993286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5444716811180115},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44714152812957764},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4151672124862671},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38054919242858887},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3579663634300232},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3284924030303955},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2708861231803894},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11175021529197693}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6737675666809082},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.6329585909843445},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5500279664993286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5444716811180115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44714152812957764},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4151672124862671},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38054919242858887},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3579663634300232},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3284924030303955},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2708861231803894},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11175021529197693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10817-012-9256-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-012-9256-3","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"Journal of Automated Reasoning","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W26772505","https://openalex.org/W102301403","https://openalex.org/W274753623","https://openalex.org/W285242605","https://openalex.org/W589984754","https://openalex.org/W791585209","https://openalex.org/W851107164","https://openalex.org/W1490012302","https://openalex.org/W1501825542","https://openalex.org/W1508667117","https://openalex.org/W1527253569","https://openalex.org/W1528172624","https://openalex.org/W1534704094","https://openalex.org/W1534850143","https://openalex.org/W1538068999","https://openalex.org/W1553142094","https://openalex.org/W1558198085","https://openalex.org/W1572998018","https://openalex.org/W1599525342","https://openalex.org/W1652501836","https://openalex.org/W1663239154","https://openalex.org/W1967184028","https://openalex.org/W1977336460","https://openalex.org/W2005536816","https://openalex.org/W2008288068","https://openalex.org/W2016389104","https://openalex.org/W2019882358","https://openalex.org/W2022441937","https://openalex.org/W2026110825","https://openalex.org/W2073787328","https://openalex.org/W2079220326","https://openalex.org/W2092808221","https://openalex.org/W2117315082","https://openalex.org/W2124497430","https://openalex.org/W2131845859","https://openalex.org/W2132303335","https://openalex.org/W2145500708","https://openalex.org/W2180832646","https://openalex.org/W2182997761","https://openalex.org/W2346492432","https://openalex.org/W2407619777","https://openalex.org/W2913574351","https://openalex.org/W2913752259","https://openalex.org/W3135109640","https://openalex.org/W3217399827","https://openalex.org/W4229917934","https://openalex.org/W4247922331","https://openalex.org/W4298290503"],"related_works":["https://openalex.org/W3206709119","https://openalex.org/W2126394356","https://openalex.org/W2062195135","https://openalex.org/W2144235323","https://openalex.org/W2189312062","https://openalex.org/W2367161241","https://openalex.org/W1578479275","https://openalex.org/W91521151","https://openalex.org/W2361696322","https://openalex.org/W2043650433"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}
