{"id":"https://openalex.org/W2545591538","doi":"https://doi.org/10.1137/16m1057322","title":"Polynomial Interpolation in Higher Dimension: From Simplicial Complexes to GC Sets","display_name":"Polynomial Interpolation in Higher Dimension: From Simplicial Complexes to GC Sets","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2545591538","doi":"https://doi.org/10.1137/16m1057322","mag":"2545591538"},"language":"en","primary_location":{"id":"doi:10.1137/16m1057322","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1057322","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.06851","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063707677","display_name":"Nathan Fieldsteel","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathan Fieldsteel","raw_affiliation_strings":["***University of Illinois at Urbana-Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"***University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038521689","display_name":"Hal Schenck","orcid":"https://orcid.org/0000-0002-1692-7500"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hal Schenck","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05349978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"1","first_page":"131","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9997000098228455,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9980999827384949,"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/dimension","display_name":"Dimension (graph theory)","score":0.7834514379501343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7031053304672241},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6058368682861328},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.566136360168457},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5504693388938904},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.5162755846977234},{"id":"https://openalex.org/keywords/simplicial-manifold","display_name":"Simplicial manifold","score":0.4943065643310547},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.49297356605529785},{"id":"https://openalex.org/keywords/simplicial-approximation-theorem","display_name":"Simplicial approximation theorem","score":0.4726770520210266},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.47232550382614136},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32082733511924744},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.27316972613334656},{"id":"https://openalex.org/keywords/simplicial-set","display_name":"Simplicial set","score":0.19735035300254822},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18061107397079468},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13472729921340942},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.07873266935348511},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.07795077562332153},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07321283221244812}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7834514379501343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7031053304672241},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6058368682861328},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.566136360168457},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5504693388938904},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5162755846977234},{"id":"https://openalex.org/C97172818","wikidata":"https://www.wikidata.org/wiki/Q7520904","display_name":"Simplicial manifold","level":5,"score":0.4943065643310547},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.49297356605529785},{"id":"https://openalex.org/C64245159","wikidata":"https://www.wikidata.org/wiki/Q3983972","display_name":"Simplicial approximation theorem","level":5,"score":0.4726770520210266},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.47232550382614136},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32082733511924744},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.27316972613334656},{"id":"https://openalex.org/C155366967","wikidata":"https://www.wikidata.org/wiki/Q1467124","display_name":"Simplicial set","level":4,"score":0.19735035300254822},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18061107397079468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13472729921340942},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.07873266935348511},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.07795077562332153},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07321283221244812},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.0},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1057322","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1057322","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1610.06851","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1610.06851","pdf_url":"https://arxiv.org/pdf/1610.06851","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2545591538","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1610.06851.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1610.06851","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1610.06851","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.06851","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1610.06851","pdf_url":"https://arxiv.org/pdf/1610.06851","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6858974980","display_name":null,"funder_award_id":"1312071","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2545591538.pdf","grobid_xml":"https://content.openalex.org/works/W2545591538.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W116293564","https://openalex.org/W1555542949","https://openalex.org/W1967468678","https://openalex.org/W1983859185","https://openalex.org/W1986155058","https://openalex.org/W1993558041","https://openalex.org/W1994817429","https://openalex.org/W2000210554","https://openalex.org/W2034332982","https://openalex.org/W2044837129","https://openalex.org/W2045932400","https://openalex.org/W2059441192","https://openalex.org/W2064840977","https://openalex.org/W2075498078","https://openalex.org/W2118468054","https://openalex.org/W2135359007","https://openalex.org/W2264065105","https://openalex.org/W2470380519","https://openalex.org/W2782831483","https://openalex.org/W3101783122","https://openalex.org/W4236478587"],"related_works":["https://openalex.org/W2962699719","https://openalex.org/W2950408786","https://openalex.org/W2265024261","https://openalex.org/W3100889865","https://openalex.org/W2979969169","https://openalex.org/W3204859624","https://openalex.org/W1964474191","https://openalex.org/W3161830121","https://openalex.org/W2075311067","https://openalex.org/W2885395027","https://openalex.org/W2964170533","https://openalex.org/W2304796618","https://openalex.org/W2027007352","https://openalex.org/W2005662535","https://openalex.org/W3127404063","https://openalex.org/W2006169827","https://openalex.org/W2110954261","https://openalex.org/W3210399983","https://openalex.org/W2563923141","https://openalex.org/W2808354904"],"abstract_inverted_index":{"Geometrically":[0],"characterized":[1],"(GC)":[2],"sets":[3,25,52,66],"were":[4],"introduced":[5],"by":[6,29,41,45],"Chung":[7],"and":[8,31,37,44,47,58],"Yao":[9],"in":[10,16,38,53],"their":[11],"work":[12],"on":[13,20],"polynomial":[14],"interpolation":[15],"$\\mathbb":[17],"R^d$.":[18],"Conjectures":[19],"the":[21,34,69],"structure":[22],"of":[23,71],"GC":[24,51],"have":[26],"been":[27],"proposed":[28],"Gasca":[30],"Maeztu":[32],"for":[33],"planar":[35],"case,":[36],"higher":[39],"dimension":[40,54],"de":[42],"Boor":[43],"Apozyan":[46],"Hakopian.":[48],"We":[49],"investigate":[50],"three":[55],"or":[56],"higher,":[57],"show":[59],"that":[60],"one":[61],"way":[62],"to":[63],"obtain":[64],"such":[65],"is":[67],"from":[68],"combinatorics":[70],"simplicial":[72],"complexes.":[73]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
