{"id":"https://openalex.org/W4320915533","doi":"https://doi.org/10.1090/mcom/3835","title":"Pointwise error estimates and local superconvergence of Jacobi expansions","display_name":"Pointwise error estimates and local superconvergence of Jacobi expansions","publication_year":2023,"publication_date":"2023-02-15","ids":{"openalex":"https://openalex.org/W4320915533","doi":"https://doi.org/10.1090/mcom/3835"},"language":"lv","primary_location":{"id":"doi:10.1090/mcom/3835","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3835","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5002179101","display_name":"Shuhuang Xiang","orcid":"https://orcid.org/0000-0002-6727-6170"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shuhuang Xiang","raw_affiliation_strings":["School of Mathematics and Statistics, INP-LAMA, Central South University, Changsha 410083, People\u00e2\u0080\u0099s Republic of China","School of Mathematics and Statistics, INP-LAMA, Central South University, Changsha 410083, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, INP-LAMA, Central South University, Changsha 410083, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Mathematics and Statistics, INP-LAMA, Central South University, Changsha 410083, People's Republic of China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023362710","display_name":"Desong Kong","orcid":"https://orcid.org/0000-0003-1995-8086"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Desong Kong","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha 410083, People\u00e2\u0080\u0099s Republic of China","School of Mathematics and Statistics, Central South University, Changsha 410083, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha 410083, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha 410083, People's Republic of China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041321666","display_name":"Guidong Liu","orcid":"https://orcid.org/0000-0001-5356-0536"},"institutions":[{"id":"https://openalex.org/I206777745","display_name":"Nanjing Audit University","ror":"https://ror.org/04zj2bd87","country_code":"CN","type":"education","lineage":["https://openalex.org/I206777745"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guidong Liu","raw_affiliation_strings":["School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815, People\u00e2\u0080\u0099s Republic of China","School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I206777745"]},{"raw_affiliation_string":"School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815, People's Republic of China","institution_ids":["https://openalex.org/I206777745"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112395743","display_name":"Li-Lian Wang","orcid":"https://orcid.org/0000-0002-2735-9019"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Li-Lian Wang","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002179101"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":3.5845,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.92572966,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"92","issue":"342","first_page":"1747","last_page":"1778"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9975000023841858,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/algorithm","display_name":"Algorithm","score":0.6968511343002319},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40219491720199585},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3977067470550537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3483283519744873}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6968511343002319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40219491720199585},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3977067470550537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3483283519744873}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3835","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3835","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/171812","is_oa":false,"landing_page_url":"https://hdl.handle.net/10356/171812","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8700000047683716}],"awards":[{"id":"https://openalex.org/G2323628319","display_name":null,"funder_award_id":"2020zzts031","funder_id":"https://openalex.org/F4320335880","funder_display_name":"Fundamental Research Funds for Central Universities of the Central South University"},{"id":"https://openalex.org/G4567695540","display_name":null,"funder_award_id":"2020zzts031","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G662666071","display_name":null,"funder_award_id":"MOE-AcRF-Tier 1: RG15/21","funder_id":"https://openalex.org/F4320335880","funder_display_name":"Fundamental Research Funds for Central Universities of the Central South University"},{"id":"https://openalex.org/G8337014725","display_name":null,"funder_award_id":"MOE-AcRF-Tier 1: RG15/21","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320335880","display_name":"Fundamental Research Funds for Central Universities of the Central South University","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W118329571","https://openalex.org/W253307310","https://openalex.org/W341063674","https://openalex.org/W357046174","https://openalex.org/W808122538","https://openalex.org/W1635622277","https://openalex.org/W1894746618","https://openalex.org/W1971690986","https://openalex.org/W1982740015","https://openalex.org/W1987826592","https://openalex.org/W1991830771","https://openalex.org/W2000292231","https://openalex.org/W2015473053","https://openalex.org/W2039660177","https://openalex.org/W2042199582","https://openalex.org/W2044190355","https://openalex.org/W2045737730","https://openalex.org/W2053990026","https://openalex.org/W2149986522","https://openalex.org/W2163969775","https://openalex.org/W2794861262","https://openalex.org/W2899964254","https://openalex.org/W2903275484","https://openalex.org/W2963539925","https://openalex.org/W2963710662","https://openalex.org/W2998834071","https://openalex.org/W3004730415","https://openalex.org/W3014280493","https://openalex.org/W3033023462","https://openalex.org/W3118737023","https://openalex.org/W3126368577","https://openalex.org/W3163170454","https://openalex.org/W4237185860","https://openalex.org/W4239308190","https://openalex.org/W4249274673","https://openalex.org/W4253937035","https://openalex.org/W4254131494","https://openalex.org/W4295022726"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596"],"abstract_inverted_index":{"As":[0,261],"one":[1],"myth":[2],"of":[3,21,119,192,230,240,264,341],"polynomial":[4,98],"interpolation":[5,20],"and":[6,233,250,256,304,339],"quadrature,":[7],"Trefethen":[8],"[Math.":[9],"Today":[10],"(Southend-on-Sea)":[11],"47":[12],"(2011),":[13],"pp.":[14,313],"184\u2013188]":[15],"revealed":[16],"that":[17,183],"the":[18,87,96,101,154,184,222,227,234,238,241,247,252,257,268,292,297,325,337,342],"Chebyshev":[19],"<inline-formula":[22,55,106,120,157,193,270],"content-type=\"math/mathml\">":[23,56,107,121,158,194,271],"<mml:math":[24,57,108,122,159,195,272],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[25,58,109,123,160,196,273],"alttext=\"StartAbsoluteValue":[26,59],"x":[27],"minus":[28],"a":[29,60,91,150,163,188,214,262],"EndAbsoluteValue\">":[30],"<mml:semantics>":[31,64,111,130,165,200,276],"<mml:mrow>":[32,65,131,166,277],"<mml:mrow":[33,43,66,72],"class=\"MJX-TeXAtom-ORD\">":[34,44,67,73],"<mml:mo":[35,45,68,74,132,140],"stretchy=\"false\">|</mml:mo>":[36,46,69,75],"</mml:mrow>":[37,47,48,70,76,79,142,171,283],"<mml:mi>x</mml:mi>":[38,167],"<mml:mo>":[39,134,279],"\u2212":[40,135],"</mml:mo>":[41,136,281],"<mml:mi>a</mml:mi>":[42,71,169],"<mml:annotation":[49,80,113,143,172,205,284],"encoding=\"application/x-tex\">|x-a|</mml:annotation>":[50],"</mml:semantics>":[51,82,115,145,174,207,287],"</mml:math>":[52,83,116,146,175,208,288],"</inline-formula>":[53,84,117,147,176,209,289],"(with":[54],"EndAbsoluteValue":[61],"greater-than":[62],"1\">":[63],"<mml:mo>&gt;</mml:mo>":[77],"<mml:mn>1</mml:mn>":[78,137,139],"encoding=\"application/x-tex\">|a|&gt;1</mml:annotation>":[81],")":[85],"at":[86],"Clenshaw-Curtis":[88],"points":[89],"exhibited":[90],"much":[92],"smaller":[93],"error":[94,224,294],"than":[95],"best":[97],"approximation":[99],"(in":[100],"maximum":[102],"norm)":[103],"in":[104,254,291,302],"about":[105],"alttext=\"95\">":[110],"<mml:mn>95</mml:mn>":[112],"encoding=\"application/x-tex\">95%</mml:annotation>":[114],"range":[118],"alttext=\"left-bracket":[124],"negative":[125],"1":[126,128],"comma":[127],"right-bracket\">":[129],"stretchy=\"false\">[</mml:mo>":[133],"<mml:mo>,</mml:mo>":[138],"stretchy=\"false\">]</mml:mo>":[141],"encoding=\"application/x-tex\">[-1,1]</mml:annotation>":[144],"except":[148],"for":[149,187,296],"small":[151],"neighbourhood":[152],"near":[153],"singular":[155],"point":[156],"alttext=\"x":[161],"equals":[162],"period\">":[164],"<mml:mo>=</mml:mo>":[168],"<mml:mo>.</mml:mo>":[170],"encoding=\"application/x-tex\">x=a.</mml:annotation>":[173],"In":[177],"this":[178,265],"paper,":[179],"we":[180],"rigorously":[181],"show":[182,251],"Jacobi":[185,231],"expansion":[186,299],"more":[189],"general":[190],"class":[191],"alttext=\"normal":[197],"upper":[198],"Phi\">":[199],"<mml:mi":[201],"mathvariant=\"normal\">":[202],"\u03a6":[203],"</mml:mi>":[204],"encoding=\"application/x-tex\">\\Phi</mml:annotation>":[206],"-functions":[210],"also":[211,245],"enjoys":[212],"such":[213],"local":[215,248],"convergence":[216],"behaviour.":[217],"Our":[218],"assertion":[219],"draws":[220],"on":[221,237],"pointwise":[223,293],"estimate":[225,295],"using":[226],"reproducing":[228],"kernel":[229],"polynomials":[232],"Hilb-type":[235],"formula":[236],"asymptotic":[239],"Bessel":[242],"transforms.":[243],"We":[244,330],"study":[246],"superconvergence":[249],"gain":[253],"order":[255],"subregions":[258],"it":[259],"occurs.":[260],"by-product":[263],"new":[266],"argument,":[267],"undesired":[269],"alttext=\"log":[274],"n\">":[275],"<mml:mi>log</mml:mi>":[278],"\u2061":[280],"<mml:mi>n</mml:mi>":[282],"encoding=\"application/x-tex\">\\log":[285],"n</mml:annotation>":[286],"-factor":[290],"Legendre":[298],"recently":[300],"stated":[301],"Babus\u0306ka":[303],"Hakula":[305],"[Comput.":[306],"Methods":[307],"Appl.":[308],"Mech":[309],"Engrg.":[310],"345":[311],"(2019),":[312],"748\u2013773]":[314],"can":[315],"be":[316],"removed.":[317],"Finally,":[318],"all":[319],"these":[320],"estimates":[321],"are":[322],"extended":[323],"to":[324,335],"functions":[326],"with":[327],"boundary":[328],"singularities.":[329],"provide":[331],"ample":[332],"numerical":[333],"evidences":[334],"demonstrate":[336],"optimality":[338],"sharpness":[340],"estimates.":[343]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4}],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2025-10-10T00:00:00"}
