{"id":"https://openalex.org/W3109089832","doi":"https://doi.org/10.1017/s0962492920000045","title":"Fast algorithms using orthogonal polynomials","display_name":"Fast algorithms using orthogonal polynomials","publication_year":2020,"publication_date":"2020-05-01","ids":{"openalex":"https://openalex.org/W3109089832","doi":"https://doi.org/10.1017/s0962492920000045","mag":"3109089832"},"language":"en","primary_location":{"id":"doi:10.1017/s0962492920000045","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492920000045","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","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/A5010027385","display_name":"Sheehan Olver","orcid":"https://orcid.org/0000-0001-6920-0826"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sheehan Olver","raw_affiliation_strings":["Department of Mathematics, Imperial College, London SW7 2AZ, UK E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College, London SW7 2AZ, UK E-mail:","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028926429","display_name":"Richard Mika\u00ebl Slevinsky","orcid":null},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Richard Mika\u00ebl Slevinsky","raw_affiliation_strings":["Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2M8 E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2M8 E-mail:","institution_ids":["https://openalex.org/I46247651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003110773","display_name":"Alex Townsend","orcid":"https://orcid.org/0000-0002-8183-7077"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alex Townsend","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, NY 14853, USA E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY 14853, USA E-mail:","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7823,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.91283914,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"29","issue":null,"first_page":"573","last_page":"699"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9994999766349792,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.6514295339584351},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6143189668655396},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5530598163604736},{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.5247214436531067},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.517676830291748},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.4853750467300415},{"id":"https://openalex.org/keywords/gauss\u2013jacobi-quadrature","display_name":"Gauss\u2013Jacobi quadrature","score":0.4736897945404053},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.43638864159584045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42927655577659607},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4205089509487152},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.4166654348373413},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38148033618927},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.276347279548645},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.25189560651779175},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.24592003226280212},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22135236859321594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1423826515674591},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06641596555709839}],"concepts":[{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.6514295339584351},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6143189668655396},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5530598163604736},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.5247214436531067},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.517676830291748},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.4853750467300415},{"id":"https://openalex.org/C54691486","wikidata":"https://www.wikidata.org/wiki/Q5527851","display_name":"Gauss\u2013Jacobi quadrature","level":5,"score":0.4736897945404053},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.43638864159584045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42927655577659607},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4205089509487152},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.4166654348373413},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38148033618927},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.276347279548645},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.25189560651779175},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.24592003226280212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22135236859321594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1423826515674591},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06641596555709839},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0962492920000045","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492920000045","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/85269","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/85269","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"699","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":191,"referenced_works":["https://openalex.org/W99016522","https://openalex.org/W116392911","https://openalex.org/W167165788","https://openalex.org/W253784358","https://openalex.org/W321261355","https://openalex.org/W567568486","https://openalex.org/W567688176","https://openalex.org/W1036709960","https://openalex.org/W1523273974","https://openalex.org/W1542251191","https://openalex.org/W1570370571","https://openalex.org/W1583371091","https://openalex.org/W1593505867","https://openalex.org/W1601581883","https://openalex.org/W1609413062","https://openalex.org/W1678272269","https://openalex.org/W1844026322","https://openalex.org/W1900210448","https://openalex.org/W1964080902","https://openalex.org/W1967374108","https://openalex.org/W1971099220","https://openalex.org/W1972617644","https://openalex.org/W1973127220","https://openalex.org/W1976584147","https://openalex.org/W1978007800","https://openalex.org/W1978865537","https://openalex.org/W1979102510","https://openalex.org/W1980362623","https://openalex.org/W1988157981","https://openalex.org/W1991622805","https://openalex.org/W1991835897","https://openalex.org/W1992978094","https://openalex.org/W1993358632","https://openalex.org/W1995166462","https://openalex.org/W1995603386","https://openalex.org/W1996464986","https://openalex.org/W1998399936","https://openalex.org/W1999850067","https://openalex.org/W2000017501","https://openalex.org/W2002357257","https://openalex.org/W2002361004","https://openalex.org/W2002391771","https://openalex.org/W2004933271","https://openalex.org/W2005131339","https://openalex.org/W2005833836","https://openalex.org/W2008004348","https://openalex.org/W2010122118","https://openalex.org/W2010358213","https://openalex.org/W2010464263","https://openalex.org/W2010569986","https://openalex.org/W2012300893","https://openalex.org/W2012601868","https://openalex.org/W2013202519","https://openalex.org/W2013562903","https://openalex.org/W2013943932","https://openalex.org/W2014114127","https://openalex.org/W2014162479","https://openalex.org/W2015622992","https://openalex.org/W2017641901","https://openalex.org/W2019764548","https://openalex.org/W2019976205","https://openalex.org/W2020044270","https://openalex.org/W2020328455","https://openalex.org/W2025485823","https://openalex.org/W2026614141","https://openalex.org/W2029529153","https://openalex.org/W2029837479","https://openalex.org/W2032454344","https://openalex.org/W2033022456","https://openalex.org/W2035253925","https://openalex.org/W2038064355","https://openalex.org/W2039396925","https://openalex.org/W2040239232","https://openalex.org/W2041381172","https://openalex.org/W2045009210","https://openalex.org/W2045145094","https://openalex.org/W2046316701","https://openalex.org/W2048028343","https://openalex.org/W2051028236","https://openalex.org/W2052169332","https://openalex.org/W2052623210","https://openalex.org/W2054188927","https://openalex.org/W2055884139","https://openalex.org/W2060442744","https://openalex.org/W2061171222","https://openalex.org/W2063208261","https://openalex.org/W2065254635","https://openalex.org/W2068324845","https://openalex.org/W2068691075","https://openalex.org/W2070782986","https://openalex.org/W2072396164","https://openalex.org/W2073683132","https://openalex.org/W2075988806","https://openalex.org/W2079474739","https://openalex.org/W2080986154","https://openalex.org/W2081237230","https://openalex.org/W2082108265","https://openalex.org/W2082624758","https://openalex.org/W2082849992","https://openalex.org/W2083206954","https://openalex.org/W2083944885","https://openalex.org/W2084540358","https://openalex.org/W2085234101","https://openalex.org/W2085932179","https://openalex.org/W2087058805","https://openalex.org/W2087928860","https://openalex.org/W2089424594","https://openalex.org/W2089755800","https://openalex.org/W2095079569","https://openalex.org/W2095860102","https://openalex.org/W2102012445","https://openalex.org/W2102591969","https://openalex.org/W2108473871","https://openalex.org/W2115770043","https://openalex.org/W2125710273","https://openalex.org/W2126744357","https://openalex.org/W2130010995","https://openalex.org/W2132718937","https://openalex.org/W2137946669","https://openalex.org/W2138106543","https://openalex.org/W2141955292","https://openalex.org/W2149599446","https://openalex.org/W2153487479","https://openalex.org/W2158575547","https://openalex.org/W2171692351","https://openalex.org/W2250759460","https://openalex.org/W2257543660","https://openalex.org/W2258092107","https://openalex.org/W2273606872","https://openalex.org/W2276306181","https://openalex.org/W2312374746","https://openalex.org/W2313278888","https://openalex.org/W2319345516","https://openalex.org/W2330548796","https://openalex.org/W2332004090","https://openalex.org/W2347093389","https://openalex.org/W2492581980","https://openalex.org/W2504492770","https://openalex.org/W2523167803","https://openalex.org/W2569750427","https://openalex.org/W2578554495","https://openalex.org/W2613161938","https://openalex.org/W2768435914","https://openalex.org/W2774131624","https://openalex.org/W2784434132","https://openalex.org/W2798909945","https://openalex.org/W2944878488","https://openalex.org/W2962716964","https://openalex.org/W2962947414","https://openalex.org/W2962997112","https://openalex.org/W2963482772","https://openalex.org/W2963520444","https://openalex.org/W2963567562","https://openalex.org/W2963643072","https://openalex.org/W2963795429","https://openalex.org/W2963950291","https://openalex.org/W2964069030","https://openalex.org/W2964132515","https://openalex.org/W2966433303","https://openalex.org/W2967582125","https://openalex.org/W2982257723","https://openalex.org/W2989660359","https://openalex.org/W2990035746","https://openalex.org/W3009760708","https://openalex.org/W3010641450","https://openalex.org/W3016658817","https://openalex.org/W3019469558","https://openalex.org/W3034251501","https://openalex.org/W3038165843","https://openalex.org/W3045065363","https://openalex.org/W3046782287","https://openalex.org/W3098055020","https://openalex.org/W3101826276","https://openalex.org/W3104682004","https://openalex.org/W3121354812","https://openalex.org/W3145733612","https://openalex.org/W4233363368","https://openalex.org/W4236485890","https://openalex.org/W4242849907","https://openalex.org/W4248741955","https://openalex.org/W4291439952","https://openalex.org/W4298524123","https://openalex.org/W4312258136","https://openalex.org/W6648491025","https://openalex.org/W6665948791","https://openalex.org/W6675118372","https://openalex.org/W6678348379","https://openalex.org/W6678663512","https://openalex.org/W6679832728","https://openalex.org/W6748508371","https://openalex.org/W6766525439"],"related_works":["https://openalex.org/W2289189603","https://openalex.org/W1661554543","https://openalex.org/W1589938172","https://openalex.org/W2148120208","https://openalex.org/W2765175526","https://openalex.org/W2049479394","https://openalex.org/W4387847482","https://openalex.org/W4317584040","https://openalex.org/W2012315814","https://openalex.org/W2007770555"],"abstract_inverted_index":{"We":[0],"review":[1],"recent":[2],"advances":[3],"in":[4,44,52,127],"algorithms":[5],"for":[6,29,48,60,105,119],"quadrature,":[7],"transforms,":[8],"differential":[9,66],"equations":[10,14,67],"and":[11,59,64],"singular":[12,107],"integral":[13,108],"using":[15,78],"orthogonal":[16,79],"polynomials.":[17],"Quadrature":[18],"based":[19,40],"on":[20,41,57],"asymptotics":[21],"has":[22],"facilitated":[23],"optimal":[24],"complexity":[25],"quadrature":[26,33],"rules,":[27],"allowing":[28],"efficient":[30,103],"computation":[31],"of":[32,37,92,123],"rules":[34],"with":[35,89,98],"millions":[36],"nodes.":[38],"Transforms":[39],"rank":[42],"structures":[43],"change-of-basis":[45],"operators":[46],"allow":[47],"quasi-optimal":[49],"complexity,":[50],"including":[51],"multivariate":[53],"settings":[54],"such":[55],"as":[56,81],"triangles":[58],"spherical":[61],"harmonics.":[62],"Ordinary":[63],"partial":[65],"can":[68,112],"be":[69,113],"solved":[70],"via":[71],"sparse":[72],"linear":[73],"algebra":[74],"when":[75],"set":[76],"up":[77],"polynomials":[80],"a":[82,120],"basis,":[83],"provided":[84],"that":[85,125],"care":[86],"is":[87],"taken":[88],"the":[90],"weights":[91],"orthogonality.":[93],"A":[94],"similar":[95],"idea,":[96],"together":[97],"low-rank":[99],"approximation,":[100],"gives":[101],"an":[102],"method":[104],"solving":[106],"equations.":[109],"These":[110],"techniques":[111],"combined":[114],"to":[115],"produce":[116],"high-performance":[117],"codes":[118],"wide":[121],"range":[122],"problems":[124],"appear":[126],"applications.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}