{"id":"https://openalex.org/W2075832873","doi":"https://doi.org/10.1145/1837934.1837966","title":"Chebyshev interpolation polynomial-based tools for rigorous computing","display_name":"Chebyshev interpolation polynomial-based tools for rigorous computing","publication_year":2010,"publication_date":"2010-07-25","ids":{"openalex":"https://openalex.org/W2075832873","doi":"https://doi.org/10.1145/1837934.1837966","mag":"2075832873"},"language":"en","primary_location":{"id":"doi:10.1145/1837934.1837966","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837966","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ens-lyon.hal.science/ensl-00472509","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058275399","display_name":"Nicolas Brisebarre","orcid":"https://orcid.org/0000-0002-4220-2132"},"institutions":[{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Nicolas Brisebarre","raw_affiliation_strings":["LIP, Ar\u00e9naire, Lyon Cedex, France"],"affiliations":[{"raw_affiliation_string":"LIP, Ar\u00e9naire, Lyon Cedex, France","institution_ids":["https://openalex.org/I4210144566"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084830779","display_name":"Mioara Jolde\u015f","orcid":"https://orcid.org/0000-0001-7781-3745"},"institutions":[{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mioara Jolde\u015f","raw_affiliation_strings":["LIP, Ar\u00e9naire, Lyon Cedex, France"],"affiliations":[{"raw_affiliation_string":"LIP, Ar\u00e9naire, Lyon Cedex, France","institution_ids":["https://openalex.org/I4210144566"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058275399"],"corresponding_institution_ids":["https://openalex.org/I4210144566"],"apc_list":null,"apc_paid":null,"fwci":3.0747,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.91367013,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"147","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6936109662055969},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.6816878318786621},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.6609372496604919},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.6574505567550659},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.6346905827522278},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5815551280975342},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5744600296020508},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.5629446506500244},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5469555854797363},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5019698143005371},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.4874839782714844},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4788767695426941},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4637141227722168},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43669241666793823},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.42348551750183105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4045860171318054},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31843364238739014},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.15100336074829102},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14820218086242676},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10265934467315674},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07871520519256592}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6936109662055969},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.6816878318786621},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.6609372496604919},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.6574505567550659},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.6346905827522278},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5815551280975342},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5744600296020508},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.5629446506500244},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5469555854797363},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5019698143005371},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.4874839782714844},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4788767695426941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4637141227722168},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43669241666793823},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.42348551750183105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4045860171318054},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31843364238739014},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.15100336074829102},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14820218086242676},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10265934467315674},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07871520519256592},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1837934.1837966","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837966","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.615.3347","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.615.3347","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://perso.ens-lyon.fr/nicolas.brisebarre/Publi/chebModels.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:ensl-00472509v2","is_oa":true,"landing_page_url":"https://ens-lyon.hal.science/ensl-00472509","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC '10, 2010 International Symposium on Symbolic and Algebraic Computation, 2010, M\u00fcnich, Germany. pp.147-154, &#x27E8;10.1145/1837934.1837966&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:ensl-00472509v2","is_oa":true,"landing_page_url":"https://ens-lyon.hal.science/ensl-00472509","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC '10, 2010 International Symposium on Symbolic and Algebraic Computation, 2010, M\u00fcnich, Germany. pp.147-154, &#x27E8;10.1145/1837934.1837966&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W617691326","https://openalex.org/W1524383063","https://openalex.org/W1580809199","https://openalex.org/W1805381866","https://openalex.org/W1973503957","https://openalex.org/W1981115560","https://openalex.org/W1987815796","https://openalex.org/W1994097280","https://openalex.org/W1998661762","https://openalex.org/W1998798933","https://openalex.org/W2019491495","https://openalex.org/W2020804487","https://openalex.org/W2037317065","https://openalex.org/W2042513324","https://openalex.org/W2044623988","https://openalex.org/W2056522847","https://openalex.org/W2059998776","https://openalex.org/W2074193803","https://openalex.org/W2077961479","https://openalex.org/W2092176285","https://openalex.org/W2092622802","https://openalex.org/W2115740319","https://openalex.org/W2115900448","https://openalex.org/W2117395364","https://openalex.org/W2125244463","https://openalex.org/W2128817474","https://openalex.org/W2144181355","https://openalex.org/W2147811800","https://openalex.org/W2158223566","https://openalex.org/W2476153571","https://openalex.org/W2565730092","https://openalex.org/W2990556914","https://openalex.org/W3043060850","https://openalex.org/W3108043981","https://openalex.org/W4300097400","https://openalex.org/W4388215348","https://openalex.org/W6638176987","https://openalex.org/W6665700246","https://openalex.org/W6835322939","https://openalex.org/W6991953935"],"related_works":["https://openalex.org/W2021099221","https://openalex.org/W1866822838","https://openalex.org/W2054912819","https://openalex.org/W4391113243","https://openalex.org/W2179563627","https://openalex.org/W2405994222","https://openalex.org/W2011010098","https://openalex.org/W2603225589","https://openalex.org/W2081451167","https://openalex.org/W2374235543"],"abstract_inverted_index":{"Performing":[0],"numerical":[1,61],"computations,":[2],"yet":[3,113],"being":[4],"able":[5],"to":[6,31,68,92,103],"provide":[7],"rigorous":[8,44,51],"mathematical":[9],"statements":[10,71],"about":[11,72],"the":[12,58,66,73,77,116],"obtained":[13],"result,":[14],"is":[15],"required":[16],"in":[17,115],"many":[18],"domains":[19],"like":[20],"global":[21],"optimization,":[22],"ODE":[23],"solving":[24],"or":[25],"integration.":[26],"Taylor":[27,39,104],"models,":[28,105],"which":[29],"associate":[30],"a":[32,34,38,43,48,89,93],"function":[33],"pair":[35],"made":[36],"of":[37,60,118],"approximation":[40,80,91],"polynomial":[41],"and":[42],"remainder":[45],"bound,":[46],"are":[47],"widely":[49],"used":[50],"computation":[52],"tool.":[53],"This":[54],"approach":[55],"benefits":[56],"from":[57],"advantages":[59],"methods,":[62],"but":[63],"also":[64],"gives":[65],"ability":[67],"make":[69],"reliable":[70],"approximated":[74],"function.":[75],"Despite":[76],"fact":[78],"that":[79],"polynomials":[81],"based":[82,106],"on":[83,107],"interpolation":[84],"at":[85],"Chebyshev":[86],"nodes":[87],"offer":[88],"quasi-optimal":[90],"function,":[94],"together":[95],"with":[96],"several":[97],"other":[98],"useful":[99],"features,":[100],"an":[101],"analogous":[102],"such":[108],"polynomials,":[109],"has":[110],"not":[111],"been":[112],"well-established":[114],"field":[117],"validated":[119],"numerics.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
