{"id":"https://openalex.org/W2147811800","doi":"https://doi.org/10.1145/1576702.1576709","title":"Chebyshev expansions for solutions of linear differential equations","display_name":"Chebyshev expansions for solutions of linear differential equations","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W2147811800","doi":"https://doi.org/10.1145/1576702.1576709","mag":"2147811800"},"language":"en","primary_location":{"id":"doi:10.1145/1576702.1576709","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576709","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0906.2888","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067804280","display_name":"Alexandre Beno\u00eet","orcid":"https://orcid.org/0000-0002-0627-4948"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Benoit","raw_affiliation_strings":["INRIA, Rocquencourt, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Rocquencourt, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047966261","display_name":"Bruno Salvy","orcid":"https://orcid.org/0000-0002-4313-0679"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bruno Salvy","raw_affiliation_strings":["INRIA, Rocquencourt, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Rocquencourt, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":1.5054,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81742606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"23","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9991999864578247,"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/T11130","display_name":"Coding theory and cryptography","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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-polynomials","display_name":"Chebyshev polynomials","score":0.7716718316078186},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.7464537620544434},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.6871943473815918},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6749441027641296},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.6602553725242615},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.6308507919311523},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.6223019957542419},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5697841644287109},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.514367938041687},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4772369861602783},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.46345752477645874},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.4461466372013092},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.4358384609222412},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41925594210624695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40162479877471924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1768496036529541},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.15920627117156982},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.130135178565979}],"concepts":[{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.7716718316078186},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.7464537620544434},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.6871943473815918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6749441027641296},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.6602553725242615},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.6308507919311523},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.6223019957542419},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5697841644287109},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.514367938041687},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4772369861602783},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.46345752477645874},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4461466372013092},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4358384609222412},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41925594210624695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40162479877471924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1768496036529541},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.15920627117156982},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.130135178565979},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/1576702.1576709","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576709","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:0906.2888","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.2888","pdf_url":"https://arxiv.org/pdf/0906.2888","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.1118","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.1118","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/0906.2888v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.412.5052","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.412.5052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/39/57/16/PDF/arxiv.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00395716v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00395716","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'09, Jul 2009, Seoul, South Korea","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0906.2888","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.2888","pdf_url":"https://arxiv.org/pdf/0906.2888","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W140628048","https://openalex.org/W222318538","https://openalex.org/W906146811","https://openalex.org/W1562183207","https://openalex.org/W2002188635","https://openalex.org/W2010830127","https://openalex.org/W2029001542","https://openalex.org/W2036494998","https://openalex.org/W2054796168","https://openalex.org/W2059998776","https://openalex.org/W2074193803","https://openalex.org/W2108473871","https://openalex.org/W2138075164","https://openalex.org/W2145476327","https://openalex.org/W2245609142","https://openalex.org/W2322908176","https://openalex.org/W2331005958","https://openalex.org/W2339153059","https://openalex.org/W2565730092","https://openalex.org/W2624619234","https://openalex.org/W4245151940","https://openalex.org/W4254246953","https://openalex.org/W4290864872"],"related_works":["https://openalex.org/W2112919228","https://openalex.org/W2136992695","https://openalex.org/W2021099221","https://openalex.org/W2054912819","https://openalex.org/W2179563627","https://openalex.org/W1974138590","https://openalex.org/W2345201752","https://openalex.org/W2034868998","https://openalex.org/W2063055382","https://openalex.org/W49014452"],"abstract_inverted_index":{"A":[0],"Chebyshev":[1,10],"expansion":[2],"is":[3],"a":[4,18,21,28,40,51,62],"series":[5,19],"in":[6],"the":[7,13,37],"basis":[8],"of":[9,12,39,42,54],"polynomials":[11],"first":[14],"kind.":[15],"When":[16],"such":[17],"solves":[20],"linear":[22,29,43],"differential":[23],"equation,":[24],"its":[25],"coefficients":[26],"satisfy":[27],"recurrence":[30,44],"equation.":[31],"We":[32],"interpret":[33],"this":[34],"equation":[35],"as":[36],"numerator":[38],"fraction":[41],"operators.":[45],"This":[46],"interpretation":[47],"lets":[48],"us":[49],"give":[50],"simple":[52],"view":[53],"previous":[55],"algorithms,":[56],"analyze":[57],"their":[58],"complexity,":[59],"and":[60],"design":[61],"faster":[63],"one":[64],"for":[65],"large":[66],"orders.":[67]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
