{"id":"https://openalex.org/W1996056542","doi":"https://doi.org/10.1090/s0025-5718-2012-02645-7","title":"On exponential convergence of Gegenbauer interpolation and spectral differentiation","display_name":"On exponential convergence of Gegenbauer interpolation and spectral differentiation","publication_year":2012,"publication_date":"2012-08-21","ids":{"openalex":"https://openalex.org/W1996056542","doi":"https://doi.org/10.1090/s0025-5718-2012-02645-7","mag":"1996056542"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02645-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02645-7","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02645-7/S0025-5718-2012-02645-7.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02645-7/S0025-5718-2012-02645-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110405587","display_name":"Ziqing Xie","orcid":"https://orcid.org/0000-0001-9372-7011"},"institutions":[{"id":"https://openalex.org/I154893126","display_name":"Guizhou Normal University","ror":"https://ror.org/02x1pa065","country_code":"CN","type":"education","lineage":["https://openalex.org/I154893126"]},{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziqing Xie","raw_affiliation_strings":["School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, China \u00e2\u0080\u0094 and \u00e2\u0080\u0094 Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China","Guizhou Normal University, Guiyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, China \u00e2\u0080\u0094 and \u00e2\u0080\u0094 Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China","institution_ids":["https://openalex.org/I154893126","https://openalex.org/I173759888"]},{"raw_affiliation_string":"Guizhou Normal University, Guiyang, China","institution_ids":["https://openalex.org/I154893126"]}]},{"author_position":"middle","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","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"]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003990800","display_name":"Xiaodan Zhao","orcid":"https://orcid.org/0000-0003-1469-8027"},"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":"Xiaodan Zhao","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","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"]},{"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":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9008,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.89557833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"82","issue":"282","first_page":"1017","last_page":"1036"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9983000159263611,"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":0.9983000159263611,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8338003754615784},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6210512518882751},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6171282529830933},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5467953681945801},{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.5152104496955872},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5026342868804932},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4790826439857483},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.44765859842300415},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4445789158344269},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44044530391693115},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.4388244152069092},{"id":"https://openalex.org/keywords/exponential-polynomial","display_name":"Exponential polynomial","score":0.43320387601852417},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.4014602303504944},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.14569535851478577},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14022275805473328},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07125702500343323}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8338003754615784},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6210512518882751},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6171282529830933},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5467953681945801},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.5152104496955872},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5026342868804932},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4790826439857483},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.44765859842300415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4445789158344269},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44044530391693115},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.4388244152069092},{"id":"https://openalex.org/C85384003","wikidata":"https://www.wikidata.org/wiki/Q5421525","display_name":"Exponential polynomial","level":3,"score":0.43320387601852417},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4014602303504944},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.14569535851478577},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14022275805473328},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07125702500343323},{"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/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02645-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02645-7","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02645-7/S0025-5718-2012-02645-7.pdf","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:CiteSeerX.psu:10.1.1.307.1183","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.1183","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2013-82-282/S0025-5718-2012-02645-7/S0025-5718-2012-02645-7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.764.9318","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.764.9318","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1109.5509.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02645-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02645-7","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02645-7/S0025-5718-2012-02645-7.pdf","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3048563442","display_name":null,"funder_award_id":"Tier 1","funder_id":"https://openalex.org/F4320320766","funder_display_name":"Nanyang Technological University"},{"id":"https://openalex.org/G8478509388","display_name":"\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4\u95f4\u65ad\u6709\u9650\u5143\u65b9\u6cd5\u7814\u7a76","funder_award_id":"11171104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1996056542.pdf","grobid_xml":"https://content.openalex.org/works/W1996056542.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W161803601","https://openalex.org/W321261355","https://openalex.org/W640428934","https://openalex.org/W1490180844","https://openalex.org/W1525628435","https://openalex.org/W1558122728","https://openalex.org/W1576246867","https://openalex.org/W1805381866","https://openalex.org/W1912930600","https://openalex.org/W1964699038","https://openalex.org/W1965328196","https://openalex.org/W1976584147","https://openalex.org/W1978958071","https://openalex.org/W1987142816","https://openalex.org/W1990792550","https://openalex.org/W1993814196","https://openalex.org/W2007801613","https://openalex.org/W2016898658","https://openalex.org/W2018426542","https://openalex.org/W2028522134","https://openalex.org/W2029337219","https://openalex.org/W2029388807","https://openalex.org/W2031567600","https://openalex.org/W2033022456","https://openalex.org/W2034008227","https://openalex.org/W2037258590","https://openalex.org/W2042333371","https://openalex.org/W2045737730","https://openalex.org/W2051745485","https://openalex.org/W2052989920","https://openalex.org/W2059998776","https://openalex.org/W2061434054","https://openalex.org/W2063440323","https://openalex.org/W2073732659","https://openalex.org/W2080870962","https://openalex.org/W2081338783","https://openalex.org/W2087512890","https://openalex.org/W2088388207","https://openalex.org/W2091336325","https://openalex.org/W2097739195","https://openalex.org/W2107979779","https://openalex.org/W2133964250","https://openalex.org/W2314359380","https://openalex.org/W2316418224","https://openalex.org/W2319345516","https://openalex.org/W2482460322","https://openalex.org/W2572060421","https://openalex.org/W2574129407","https://openalex.org/W2596323328","https://openalex.org/W3038165843","https://openalex.org/W3113221786","https://openalex.org/W4230959423","https://openalex.org/W4244176364","https://openalex.org/W4244303144","https://openalex.org/W4254246953","https://openalex.org/W4301973099","https://openalex.org/W6601817013","https://openalex.org/W6607543589","https://openalex.org/W6629284705","https://openalex.org/W6632564132","https://openalex.org/W6688038182","https://openalex.org/W6815406448"],"related_works":["https://openalex.org/W2037213994","https://openalex.org/W2493096353","https://openalex.org/W2793709684","https://openalex.org/W2489863694","https://openalex.org/W1759779713","https://openalex.org/W225326886","https://openalex.org/W2059214509","https://openalex.org/W2072647369","https://openalex.org/W66473703","https://openalex.org/W2070537393"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,28],"devoted":[3],"to":[4],"a":[5],"rigorous":[6],"analysis":[7],"of":[8,11],"exponential":[9],"convergence":[10],"polynomial":[12],"interpolation":[13],"and":[14,21,31],"spectral":[15],"differentiation":[16],"based":[17],"on":[18,30],"the":[19,25,39],"Gegenbauer-Gauss":[20],"Gegenbauer-Gauss-Lobatto":[22],"points,":[23],"when":[24],"underlying":[26],"function":[27],"analytic":[29],"within":[32],"an":[33],"ellipse.":[34],"Sharp":[35],"error":[36],"estimates":[37],"in":[38],"maximum":[40],"norm":[41],"are":[42],"derived.":[43]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}