{"id":"https://openalex.org/W2405142088","doi":"https://doi.org/10.1007/978-3-319-31769-4_14","title":"Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form","display_name":"Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2405142088","doi":"https://doi.org/10.1007/978-3-319-31769-4_14","mag":"2405142088"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-31769-4_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-31769-4_14","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/978-3-319-31769-4_14","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025979863","display_name":"J\u00fcrgen Garloff","orcid":"https://orcid.org/0000-0002-4078-1687"},"institutions":[{"id":"https://openalex.org/I9649716","display_name":"HTWG Hochschule Konstanz - Technik, Wirtschaft und Gestaltung","ror":"https://ror.org/051qw9f78","country_code":"DE","type":"education","lineage":["https://openalex.org/I9649716"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J\u00fcrgen Garloff","raw_affiliation_strings":["University of Applied Sciences/HTWG Konstanz, Konstanz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Applied Sciences/HTWG Konstanz, Konstanz, Germany","institution_ids":["https://openalex.org/I9649716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009403196","display_name":"Tareq Hamadneh","orcid":"https://orcid.org/0000-0003-1867-8111"},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tareq Hamadneh","raw_affiliation_strings":["University of Konstanz, Konstanz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Konstanz, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025979863"],"corresponding_institution_ids":["https://openalex.org/I9649716"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":8.031,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.97220556,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"171","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994999766349792,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9710000157356262,"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/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.7266877889633179},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.70571368932724},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5816423892974854},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5246757864952087},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49750664830207825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48083624243736267},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.47707903385162354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4230729937553406},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41492223739624023},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.4101424515247345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23700153827667236}],"concepts":[{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.7266877889633179},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.70571368932724},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5816423892974854},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5246757864952087},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49750664830207825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48083624243736267},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.47707903385162354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4230729937553406},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41492223739624023},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.4101424515247345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23700153827667236},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-319-31769-4_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-31769-4_14","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:kops.uni-konstanz.de:123456789/36705","is_oa":true,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:352-0-386644","pdf_url":null,"source":{"id":"https://openalex.org/S4377196311","display_name":"KOPS (University of Konstanz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189712700","host_organization_name":"University of Konstanz","host_organization_lineage":["https://openalex.org/I189712700"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1007/978-3-319-31769-4_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-31769-4_14","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6200000047683716,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W37596728","https://openalex.org/W1483874187","https://openalex.org/W1563265275","https://openalex.org/W1568122591","https://openalex.org/W1998929424","https://openalex.org/W2015611382","https://openalex.org/W2073330885","https://openalex.org/W2115344771","https://openalex.org/W2131845859","https://openalex.org/W2163270919","https://openalex.org/W2180832646","https://openalex.org/W2296409857","https://openalex.org/W2314084593"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W2326935216","https://openalex.org/W2296409857","https://openalex.org/W3158393360","https://openalex.org/W2946568754","https://openalex.org/W2378159473","https://openalex.org/W2099581135","https://openalex.org/W4281570361"],"abstract_inverted_index":{"A":[0],"method":[1],"is":[2,73],"investigated":[3],"by":[4],"which":[5],"tight":[6],"bounds":[7,40],"on":[8,25],"the":[9,26,29,39,42,50,54,57,65,69],"range":[10,43],"of":[11,28,38,49,56,68],"a":[12,17],"multivariate":[13],"rational":[14],"function":[15,72],"over":[16],"box":[18,58],"can":[19],"be":[20],"computed.":[21],"The":[22],"approach":[23],"relies":[24],"expansion":[27],"numerator":[30],"and":[31,59,64],"denominator":[32],"polynomials":[33],"in":[34],"Bernstein":[35,51],"polynomials.":[36],"Convergence":[37],"to":[41,46,53,60],"with":[44],"respect":[45],"degree":[47],"elevation":[48],"expansion,":[52],"width":[55],"subdivision":[61],"are":[62],"proven":[63],"inclusion":[66],"isotonicity":[67],"related":[70],"enclosure":[71],"shown.":[74]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-26T08:31:28.666265","created_date":"2025-10-10T00:00:00"}
