{"id":"https://openalex.org/W3000826180","doi":"https://doi.org/10.1142/s0219691320500216","title":"Simultaneous approximation of Birkhoff interpolation and the associated sharp inequalities","display_name":"Simultaneous approximation of Birkhoff interpolation and the associated sharp inequalities","publication_year":2020,"publication_date":"2020-01-22","ids":{"openalex":"https://openalex.org/W3000826180","doi":"https://doi.org/10.1142/s0219691320500216","mag":"3000826180"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691320500216","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691320500216","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","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/A5009518750","display_name":"Zehong Liu","orcid":"https://orcid.org/0009-0002-9566-3992"},"institutions":[{"id":"https://openalex.org/I15062923","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559","country_code":"CN","type":"education","lineage":["https://openalex.org/I15062923"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zehong Liu","raw_affiliation_strings":["School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China","institution_ids":["https://openalex.org/I15062923"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037359203","display_name":"Wanting Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wanting Lu","raw_affiliation_strings":["School of Mathematical Science, Capital Normal University, Beijing 100048, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Capital Normal University, Beijing 100048, P. R. China","institution_ids":["https://openalex.org/I96852419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031300526","display_name":"Guiqiao Xu","orcid":"https://orcid.org/0000-0003-1448-2963"},"institutions":[{"id":"https://openalex.org/I15062923","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559","country_code":"CN","type":"education","lineage":["https://openalex.org/I15062923"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiqiao Xu","raw_affiliation_strings":["School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China","institution_ids":["https://openalex.org/I15062923"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4461,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.53973839,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"04","first_page":"2050021","last_page":"2050021"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9975000023841858,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9898999929428101,"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/mathematics","display_name":"Mathematics","score":0.8122648000717163},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5799041986465454},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5766178369522095},{"id":"https://openalex.org/keywords/birkhoff-interpolation","display_name":"Birkhoff interpolation","score":0.5205281972885132},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4925740361213684},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.44967347383499146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3631308674812317},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32377272844314575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3150686025619507},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3147315979003906},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.25543344020843506},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.12835314869880676},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09566530585289001}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8122648000717163},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5799041986465454},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5766178369522095},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.5205281972885132},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4925740361213684},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.44967347383499146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3631308674812317},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32377272844314575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3150686025619507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3147315979003906},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.25543344020843506},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.12835314869880676},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09566530585289001},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691320500216","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691320500216","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1227297294","display_name":null,"funder_award_id":"11871006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8630104580","display_name":null,"funder_award_id":"11671271","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1598589417","https://openalex.org/W1973281194","https://openalex.org/W1981787994","https://openalex.org/W1986919984","https://openalex.org/W2023825909","https://openalex.org/W2041378548","https://openalex.org/W2043373009","https://openalex.org/W2097671948","https://openalex.org/W2120958527","https://openalex.org/W2518442835","https://openalex.org/W2624338055","https://openalex.org/W2943483385","https://openalex.org/W2949468895"],"related_works":["https://openalex.org/W2326086556","https://openalex.org/W2055064587","https://openalex.org/W2035818364","https://openalex.org/W2032944420","https://openalex.org/W2337828970","https://openalex.org/W200003053","https://openalex.org/W4239547667","https://openalex.org/W2369441324","https://openalex.org/W2992838974","https://openalex.org/W3163333561"],"abstract_inverted_index":{"This":[0],"paper":[1],"gives":[2],"a":[3,111],"kind":[4],"of":[5,11,38,60,67,74,83,99,106,110],"sharp":[6,122,129],"simultaneous":[7],"approximation":[8],"error":[9],"estimation":[10],"Birkhoff":[12,30,61],"interpolation":[13,31,48],"[Formula:":[14,17,21,25,34,40,68,84,88,100,125,132],"see":[15,18,22,26,35,41,46,69,85,89,101,126,133],"text],":[16],"text]":[19,23,27,36,42,70,86,90,102,127],"where":[20],"and":[24,87,96,128],"is":[28],"the":[29,56,65,72,81,97,104,107,115,120],"based":[32,54],"on":[33,55],"pairs":[37],"numbers":[39],"with":[43],"its":[44],"P[Formula:":[45],"text]lya":[47],"matrix":[49],"to":[50,71,91,103],"be":[51],"regular.":[52],"First,":[53],"integral":[57,76,94],"remainder":[58],"formula":[59],"interpolation,":[62],"we":[63,79,118],"refer":[64,80],"computation":[66,105],"norm":[73],"an":[75],"operator.":[77,113],"Second,":[78],"values":[82],"two":[92],"explicit":[93],"expressions":[95],"value":[98],"maximum":[108],"eigenvalue":[109],"Hilbert\u2013Schmidt":[112],"At":[114],"same":[116],"time,":[117],"give":[119],"corresponding":[121],"Wirtinger":[123],"inequality":[124,131],"Picone":[130],"text].":[134]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}