{"id":"https://openalex.org/W2004933271","doi":"https://doi.org/10.1137/070703065","title":"Computing with Expansions in Gegenbauer Polynomials","display_name":"Computing with Expansions in Gegenbauer Polynomials","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2004933271","doi":"https://doi.org/10.1137/070703065","mag":"2004933271"},"language":"en","primary_location":{"id":"doi:10.1137/070703065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070703065","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5054002931","display_name":"Jens Keiner","orcid":null},"institutions":[{"id":"https://openalex.org/I9341345","display_name":"University of L\u00fcbeck","ror":"https://ror.org/00t3r8h32","country_code":"DE","type":"education","lineage":["https://openalex.org/I9341345"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jens Keiner","raw_affiliation_strings":["keiner@math.uni-luebeck.de#TAB#"],"affiliations":[{"raw_affiliation_string":"keiner@math.uni-luebeck.de#TAB#","institution_ids":["https://openalex.org/I9341345"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054002931"],"corresponding_institution_ids":["https://openalex.org/I9341345"],"apc_list":null,"apc_paid":null,"fwci":0.7136,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.67139731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"3","first_page":"2151","last_page":"2171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9991999864578247,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9988999962806702,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9980999827384949,"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/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.859800398349762},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8181928396224976},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.7540192604064941},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.6780471801757812},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.633926272392273},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.5746992230415344},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.540190577507019},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.5391450524330139},{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.4458395838737488},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.43538615107536316},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.4189720153808594},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4168907701969147},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4114512503147125},{"id":"https://openalex.org/keywords/hahn-polynomials","display_name":"Hahn polynomials","score":0.411260724067688},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.346916526556015},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34678709506988525},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1974332630634308}],"concepts":[{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.859800398349762},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8181928396224976},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.7540192604064941},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.6780471801757812},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.633926272392273},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.5746992230415344},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.540190577507019},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.5391450524330139},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.4458395838737488},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.43538615107536316},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.4189720153808594},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4168907701969147},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4114512503147125},{"id":"https://openalex.org/C61349858","wikidata":"https://www.wikidata.org/wiki/Q1568814","display_name":"Hahn polynomials","level":5,"score":0.411260724067688},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.346916526556015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34678709506988525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1974332630634308},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070703065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070703065","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.73.6280","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.6280","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.unsw.edu.au/applied/files/2007/amr07_10.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1532632375","https://openalex.org/W1805381866","https://openalex.org/W1964699038","https://openalex.org/W1965499191","https://openalex.org/W1966453186","https://openalex.org/W1967374108","https://openalex.org/W1973312654","https://openalex.org/W1978798278","https://openalex.org/W1993029803","https://openalex.org/W2005998530","https://openalex.org/W2006326329","https://openalex.org/W2020804487","https://openalex.org/W2028125376","https://openalex.org/W2028783611","https://openalex.org/W2031614119","https://openalex.org/W2036494998","https://openalex.org/W2045145094","https://openalex.org/W2052169332","https://openalex.org/W2053084411","https://openalex.org/W2070782986","https://openalex.org/W2083206954","https://openalex.org/W2102182691","https://openalex.org/W2112623636","https://openalex.org/W2115770043","https://openalex.org/W2120062331","https://openalex.org/W2149599446","https://openalex.org/W2160615084","https://openalex.org/W2169004268","https://openalex.org/W2341059552","https://openalex.org/W2569750427","https://openalex.org/W2951588113","https://openalex.org/W2953873138","https://openalex.org/W2967582125","https://openalex.org/W3038165843","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2072647369","https://openalex.org/W2493096353","https://openalex.org/W2070537393","https://openalex.org/W2045154321","https://openalex.org/W2168893271","https://openalex.org/W2158826266","https://openalex.org/W2132314122","https://openalex.org/W34992575","https://openalex.org/W3147630167","https://openalex.org/W2963004660"],"abstract_inverted_index":{"We":[0],"develop":[1],"fast":[2],"algorithms":[3],"for":[4,73,82],"computations":[5],"involving":[6,53],"finite":[7,19],"expansions":[8,77],"in":[9],"Gegenbauer":[10,25,49,89],"polynomials.":[11,26],"A":[12],"method":[13],"is":[14,34,38],"described":[15],"to":[16],"convert":[17],"any":[18],"expansion":[20,30],"between":[21],"different":[22],"families":[23],"of":[24,56,76,88],"For":[27],"a":[28,86],"degree-n":[29],"the":[31,39,47,74,83],"computational":[32],"cost":[33],"$\\mathcal{O}(n(\\log(1/\\varepsilon)+|\\alpha-\\beta|))$,":[35],"where":[36],"$\\varepsilon$":[37],"prescribed":[40,79],"accuracy,":[41],"and":[42,44,81],"$\\alpha$":[43],"$\\beta$":[45],"are":[46,59],"respective":[48],"indices.":[50],"Special":[51],"cases":[52],"Chebyshev":[54],"polynomials":[55,90],"first":[57],"kind":[58],"particularly":[60],"important.":[61],"In":[62],"combination":[63],"with":[64],"(nonequispaced)":[65],"discrete":[66],"cosine":[67],"transforms,":[68],"we":[69],"obtain":[70],"efficient":[71],"methods":[72],"evaluation":[75],"at":[78],"nodes,":[80],"projection":[84],"onto":[85],"sequence":[87],"from":[91],"given":[92],"function":[93],"values,":[94],"respectively.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
