{"id":"https://openalex.org/W4367055221","doi":"https://doi.org/10.1137/22m1481452","title":"Analysis of Error Localization of Chebyshev Spectral Approximations","display_name":"Analysis of Error Localization of Chebyshev Spectral Approximations","publication_year":2023,"publication_date":"2023-04-26","ids":{"openalex":"https://openalex.org/W4367055221","doi":"https://doi.org/10.1137/22m1481452"},"language":"en","primary_location":{"id":"doi:10.1137/22m1481452","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1481452","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":"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/A5070318438","display_name":"Haiyong Wang","orcid":"https://orcid.org/0000-0002-0360-4489"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haiyong Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People\u2019s Republic of China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, People\u2019s Republic of China","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-0360-4489","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People\u2019s Republic of China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, People\u2019s Republic of China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070318438"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":6.7705,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.98396794,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"61","issue":"2","first_page":"952","last_page":"972"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976999759674072,"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/chebyshev-filter","display_name":"Chebyshev filter","score":0.8614356517791748},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8164587020874023},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.7871783971786499},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.6058541536331177},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5439460277557373},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5310730338096619},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.5293430089950562},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5271976590156555},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.5238425731658936},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.4933151304721832},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.433468759059906},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.08932003378868103}],"concepts":[{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.8614356517791748},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8164587020874023},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7871783971786499},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.6058541536331177},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5439460277557373},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5310730338096619},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.5293430089950562},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5271976590156555},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.5238425731658936},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.4933151304721832},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.433468759059906},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.08932003378868103},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1481452","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1481452","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6365469523","display_name":null,"funder_award_id":"11671160","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":33,"referenced_works":["https://openalex.org/W253307310","https://openalex.org/W1490180844","https://openalex.org/W1512638263","https://openalex.org/W1567668233","https://openalex.org/W1595515622","https://openalex.org/W1805381866","https://openalex.org/W1967779414","https://openalex.org/W1972485395","https://openalex.org/W1979771852","https://openalex.org/W1980026162","https://openalex.org/W1981115560","https://openalex.org/W2015473053","https://openalex.org/W2020038360","https://openalex.org/W2029776525","https://openalex.org/W2033022456","https://openalex.org/W2044190355","https://openalex.org/W2056522847","https://openalex.org/W2068324845","https://openalex.org/W2070256299","https://openalex.org/W2095523361","https://openalex.org/W2102591969","https://openalex.org/W2116581862","https://openalex.org/W2117934866","https://openalex.org/W2476153571","https://openalex.org/W2767434258","https://openalex.org/W2903275484","https://openalex.org/W3014280493","https://openalex.org/W3118737023","https://openalex.org/W3126368577","https://openalex.org/W4247375400","https://openalex.org/W4253937035","https://openalex.org/W4293215241","https://openalex.org/W4295022726"],"related_works":["https://openalex.org/W2054912819","https://openalex.org/W2021099221","https://openalex.org/W49014452","https://openalex.org/W1976132774","https://openalex.org/W2179563627","https://openalex.org/W2039062045","https://openalex.org/W2025186172","https://openalex.org/W2103708249","https://openalex.org/W2035026539","https://openalex.org/W4367055221"],"abstract_inverted_index":{".Chebyshev":[0],"spectral":[1,121,141],"methods":[2],"are":[3,42],"widely":[4],"used":[5],"in":[6,21,36,150,157,166,179],"numerical":[7],"computations.":[8],"When":[9],"the":[10,40,68,83,95,103,112,154,158,162,167,180],"underlying":[11],"function":[12],"has":[13],"a":[14,37,53,63,99,135,151],"singularity,":[15],"it":[16],"was":[17],"observed":[18],"by":[19],"Trefethen":[20],"2011":[22],"that":[23,32,67,92,139],"its":[24],"Chebyshev":[25,58,73,107,118,120,140],"interpolants":[26],"exhibit":[27],"an":[28],"error":[29,55,104,129,184],"localization":[30,105,130],"property,":[31],"is,":[33],"their":[34,128,146,176],"errors":[35],"neighborhood":[38,152],"of":[39,60,70,72,75,88,93,106,114,153,169],"singularity":[41,64,84,155,163],"obviously":[43],"larger":[44],"than":[45,91,145,175],"elsewhere.":[46],"In":[47],"this":[48],"paper,":[49],"we":[50,137],"first":[51],"present":[52],"pointwise":[54],"analysis":[56,116],"for":[57,102],"projections":[59,74,125],"functions":[61],"with":[62],"and":[65,123,126],"prove":[66],"rate":[69],"convergence":[71],"degree":[76],"\\(n\\)":[77,89],"at":[78,94],"each":[79],"point":[80],"away":[81],"from":[82],"is":[85,164],"one":[86],"power":[87],"faster":[90,144,174],"singularity.":[96],"This":[97],"gives":[98],"rigorous":[100],"justification":[101],"projections.":[108],"We":[109],"then":[110],"extend":[111],"framework":[113],"our":[115],"to":[117],"interpolants,":[119],"differentiations,":[122],"Legendre":[124],"justify":[127],"using":[131],"similar":[132],"arguments.":[133],"As":[134],"result,":[136],"find":[138],"differentiations":[142],"converge":[143,172],"best":[147,177],"counterparts":[148,178],"except":[149],"and,":[156],"particular":[159],"case":[160],"where":[161],"located":[165],"interior":[168],"interval,":[170],"they":[171],"even":[173],"maximum":[181],"norm.KeywordsChebyshev":[182],"projectionspointwise":[183],"estimateserror":[185],"localizationbest":[186],"approximationsChebyshev":[187],"interpolantsspectral":[188],"differentiationLegendre":[189],"projectionsMSC":[190],"codes41A1041A2541A50":[191]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}