{"id":"https://openalex.org/W2092967342","doi":"https://doi.org/10.1090/s0025-5718-05-01774-6","title":"On computing rational Gauss-Chebyshev quadrature formulas","display_name":"On computing rational Gauss-Chebyshev quadrature formulas","publication_year":2005,"publication_date":"2005-10-04","ids":{"openalex":"https://openalex.org/W2092967342","doi":"https://doi.org/10.1090/s0025-5718-05-01774-6","mag":"2092967342"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01774-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01774-6","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01774-6/S0025-5718-05-01774-6.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01774-6/S0025-5718-05-01774-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001358666","display_name":"Joris Van Deun","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Joris Van Deun","raw_affiliation_strings":["Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium","Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089712696","display_name":"Adhemar Bultheel","orcid":"https://orcid.org/0000-0001-9562-5297"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Adhemar Bultheel","raw_affiliation_strings":["Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium","Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Department of Computer Science, K.U.Leuven, B-3001 Heverlee, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027628636","display_name":"Pablo Gonz\u00e1lez Vera","orcid":null},"institutions":[{"id":"https://openalex.org/I158438070","display_name":"Universidad de La Laguna","ror":"https://ror.org/01r9z8p25","country_code":"ES","type":"education","lineage":["https://openalex.org/I158438070"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Pablo Gonz\u00e1lez Vera","raw_affiliation_strings":["Depto. An\u00e1lisis Matem\u00e1tico, Univ. La Laguna, 38206 La Laguna, Tenerife, Canary Islands, Spain"],"affiliations":[{"raw_affiliation_string":"Depto. An\u00e1lisis Matem\u00e1tico, Univ. La Laguna, 38206 La Laguna, Tenerife, Canary Islands, Spain","institution_ids":["https://openalex.org/I158438070"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001358666"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":7.01,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.97904276,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"75","issue":"253","first_page":"307","last_page":"326"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9991999864578247,"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":0.9991999864578247,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9959999918937683,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955000281333923,"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/algorithm","display_name":"Algorithm","score":0.7019972801208496},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.43936488032341003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4280349314212799},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3877822756767273},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15007063746452332}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7019972801208496},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.43936488032341003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4280349314212799},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3877822756767273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15007063746452332}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-05-01774-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01774-6","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01774-6/S0025-5718-05-01774-6.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.109.3996","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.3996","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/mcom/2006-75-253/S0025-5718-05-01774-6/S0025-5718-05-01774-6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.5190","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.5190","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/2008-77-262/S0025-5718-07-01982-5/S0025-5718-07-01982-5.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.503.9015","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.503.9015","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://lirias.kuleuven.be/bitstream/123456789/183155/1/tw448.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.8446","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.8446","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.kuleuven.ac.be/cwis/research/nalag/papers/ade/gausscheb/cheb.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01774-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01774-6","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01774-6/S0025-5718-05-01774-6.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321454","display_name":"Belgian Federal Science Policy Office","ror":"https://ror.org/01fapfv42"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2092967342.pdf","grobid_xml":"https://content.openalex.org/works/W2092967342.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W130249170","https://openalex.org/W1572758332","https://openalex.org/W1883951665","https://openalex.org/W1984907140","https://openalex.org/W1996464986","https://openalex.org/W1997520325","https://openalex.org/W2003166665","https://openalex.org/W2005715758","https://openalex.org/W2030029320","https://openalex.org/W2033904399","https://openalex.org/W2035253925","https://openalex.org/W2041634741","https://openalex.org/W2058626020","https://openalex.org/W2067097725","https://openalex.org/W2090130359","https://openalex.org/W2116522231","https://openalex.org/W2147522142","https://openalex.org/W2160471186","https://openalex.org/W3038165843","https://openalex.org/W3102685339","https://openalex.org/W4214941430","https://openalex.org/W4247696986","https://openalex.org/W4252506853"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"We":[0],"provide":[1],"an":[2],"algorithm":[3],"to":[4,56],"compute":[5],"the":[6,61,77,84,118,132],"nodes":[7],"and":[8,72],"weights":[9],"for":[10,68,123],"Gauss-Chebyshev":[11],"quadrature":[12,59],"formulas":[13],"integrating":[14],"exactly":[15],"in":[16],"spaces":[17],"of":[18,87,120,135],"rational":[19,58,126,139],"functions":[20,140],"with":[21,170],"arbitrary":[22,171],"real":[23,172],"poles":[24,78,173],"outside":[25,174],"<inline-formula":[26,89,142],"content-type=\"math/mathml\">":[27,90,143],"<mml:math":[28,91,144],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[29,92,145],"alttext=\"left-bracket":[30,146],"negative":[31,147],"1":[32,34,148,150],"comma":[33,149],"right-bracket\">":[35,151],"<mml:semantics>":[36,98,152],"<mml:mrow>":[37,99,153],"<mml:mo":[38,46,101,104,154,162],"stretchy=\"false\">[</mml:mo>":[39,155],"<mml:mo>":[40,156],"\u2212":[41,157],"</mml:mo>":[42,158],"<mml:mn>1</mml:mn>":[43,45,159,161],"<mml:mo>,</mml:mo>":[44,160],"stretchy=\"false\">]</mml:mo>":[47,163],"</mml:mrow>":[48,106,164],"<mml:annotation":[49,107,165],"encoding=\"application/x-tex\">[-1,1]</mml:annotation>":[50,166],"</mml:semantics>":[51,109,167],"</mml:math>":[52,110,168],"</inline-formula>":[53,111,169],".":[54,112],"Contrary":[55],"existing":[57],"formulas,":[60],"computational":[62],"effort":[63],"is":[64,86,115],"very":[65],"low,":[66],"even":[67],"extremely":[69],"high":[70],"degrees,":[71],"under":[73],"certain":[74],"conditions":[75],"on":[76,117,141],"it":[79],"can":[80],"be":[81],"shown":[82],"that":[83],"complexity":[85],"order":[88],"alttext=\"upper":[93],"O":[94],"left-parenthesis":[95],"n":[96],"right-parenthesis\">":[97],"<mml:mi>O</mml:mi>":[100],"stretchy=\"false\">(</mml:mo>":[102],"<mml:mi>n</mml:mi>":[103],"stretchy=\"false\">)</mml:mo>":[105],"encoding=\"application/x-tex\">O(n)</mml:annotation>":[108],"This":[113],"method":[114],"based":[116],"derivation":[119],"explicit":[121],"expressions":[122],"Chebyshev":[124],"orthogonal":[125,138],"functions,":[127],"which":[128],"are":[129],"(thus":[130],"far)":[131],"only":[133],"examples":[134],"explicitly":[136],"known":[137],"this":[175],"interval.":[176]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
