{"id":"https://openalex.org/W2006069011","doi":"https://doi.org/10.1137/130931035","title":"Numerical Algorithms Based on Analytic Function Values at Roots of Unity","display_name":"Numerical Algorithms Based on Analytic Function Values at Roots of Unity","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2006069011","doi":"https://doi.org/10.1137/130931035","mag":"2006069011"},"language":"en","primary_location":{"id":"doi:10.1137/130931035","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130931035","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/463531","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049730032","display_name":"Anthony P. Austin","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Anthony P. Austin","raw_affiliation_strings":["Oxford University Mathematical Institute, Oxford OX2 6GG, UK"],"affiliations":[{"raw_affiliation_string":"Oxford University Mathematical Institute, Oxford OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113785844","display_name":"Peter Kravanja","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":false,"raw_author_name":"Peter Kravanja","raw_affiliation_strings":["Department of Computer Science, Katholieke Universiteit Leuven, 3001 Heverlee, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Katholieke Universiteit Leuven, 3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065363123","display_name":"Lloyd N. Trefethen","orcid":"https://orcid.org/0000-0003-2504-1709"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lloyd N. Trefethen","raw_affiliation_strings":["Oxford University Mathematical Institute, Oxford OX2 6GG, UK"],"affiliations":[{"raw_affiliation_string":"Oxford University Mathematical Institute, Oxford OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049730032"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":14.6701,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.99539653,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"52","issue":"4","first_page":"1795","last_page":"1821"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9972000122070312,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9961000084877014,"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/mathematics","display_name":"Mathematics","score":0.8526674509048462},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.7091182470321655},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.6992940902709961},{"id":"https://openalex.org/keywords/meromorphic-function","display_name":"Meromorphic function","score":0.6117358207702637},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5966610908508301},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5824834108352661},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.535825252532959},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5119541883468628},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5104621648788452},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5098406672477722},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3581044375896454},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3396530747413635},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28400808572769165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8526674509048462},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.7091182470321655},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.6992940902709961},{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.6117358207702637},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5966610908508301},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5824834108352661},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.535825252532959},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5119541883468628},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5104621648788452},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5098406672477722},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3581044375896454},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3396530747413635},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28400808572769165},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/130931035","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130931035","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/463531","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/463531","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, vol. 52 (4), (1795-1821)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:uuid:f58b4eb8-94f3-4afd-bc32-8edf44835927","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/","raw_type":"Technical Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.386.3018","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.386.3018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.maths.ox.ac.uk/trefethen/austin_kravanja_trefethen.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.644.2973","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.644.2973","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.maths.ox.ac.uk/trefethen/austin_kravanja_trefethen_revised.pdf","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:f58b4eb8-94f3-4afd-bc32-8edf44835927","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:f58b4eb8-94f3-4afd-bc32-8edf44835927","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/","raw_type":"Report"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/463531","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/463531","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, vol. 52 (4), (1795-1821)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":87,"referenced_works":["https://openalex.org/W19451620","https://openalex.org/W21261701","https://openalex.org/W24774088","https://openalex.org/W84119631","https://openalex.org/W110936609","https://openalex.org/W253307310","https://openalex.org/W384065554","https://openalex.org/W576978095","https://openalex.org/W628177418","https://openalex.org/W1498751840","https://openalex.org/W1551480811","https://openalex.org/W1590577697","https://openalex.org/W1592106811","https://openalex.org/W1647470094","https://openalex.org/W1713044966","https://openalex.org/W1963833004","https://openalex.org/W1966992674","https://openalex.org/W1967332578","https://openalex.org/W1972936389","https://openalex.org/W1972978085","https://openalex.org/W1974176001","https://openalex.org/W1974322848","https://openalex.org/W1975685554","https://openalex.org/W1975959460","https://openalex.org/W1976402907","https://openalex.org/W1981115560","https://openalex.org/W1984714339","https://openalex.org/W1987941491","https://openalex.org/W1988150292","https://openalex.org/W1988452081","https://openalex.org/W1994494591","https://openalex.org/W1996087276","https://openalex.org/W1998527589","https://openalex.org/W1998906317","https://openalex.org/W2004797340","https://openalex.org/W2006962396","https://openalex.org/W2011632194","https://openalex.org/W2014989235","https://openalex.org/W2015140058","https://openalex.org/W2018685232","https://openalex.org/W2019468180","https://openalex.org/W2024431688","https://openalex.org/W2025613766","https://openalex.org/W2027319740","https://openalex.org/W2028833374","https://openalex.org/W2030762303","https://openalex.org/W2031968565","https://openalex.org/W2043384640","https://openalex.org/W2046011269","https://openalex.org/W2046319229","https://openalex.org/W2049897010","https://openalex.org/W2053944839","https://openalex.org/W2055757595","https://openalex.org/W2056522847","https://openalex.org/W2062486712","https://openalex.org/W2064610948","https://openalex.org/W2066855946","https://openalex.org/W2069970858","https://openalex.org/W2073773252","https://openalex.org/W2077687454","https://openalex.org/W2077962987","https://openalex.org/W2081719420","https://openalex.org/W2087058805","https://openalex.org/W2087255259","https://openalex.org/W2090135316","https://openalex.org/W2113289243","https://openalex.org/W2117648842","https://openalex.org/W2122706558","https://openalex.org/W2138249740","https://openalex.org/W2141243691","https://openalex.org/W2143164363","https://openalex.org/W2152538969","https://openalex.org/W2161323164","https://openalex.org/W2171042498","https://openalex.org/W2268201048","https://openalex.org/W2313120213","https://openalex.org/W2326826799","https://openalex.org/W2332202058","https://openalex.org/W2401629257","https://openalex.org/W2478312551","https://openalex.org/W2504492770","https://openalex.org/W2566416464","https://openalex.org/W2963315512","https://openalex.org/W2964332084","https://openalex.org/W3100091305","https://openalex.org/W3102642423","https://openalex.org/W4206339480"],"related_works":["https://openalex.org/W1588903465","https://openalex.org/W4286770557","https://openalex.org/W2952227491","https://openalex.org/W1497735364","https://openalex.org/W1968067346","https://openalex.org/W3097857285","https://openalex.org/W2086918857","https://openalex.org/W1495823515","https://openalex.org/W2010341774","https://openalex.org/W2950118224"],"abstract_inverted_index":{"Let":[0],"$f(z)$":[1,29],"be":[2],"an":[3],"analytic":[4],"or":[5,30,45,94],"meromorphic":[6],"function":[7],"in":[8,36,49,55,67,121,137],"the":[9,15,37,43,50,56,83,87,115,119,122,133],"closed":[10],"unit":[11],"disk":[12,123],"sampled":[13],"at":[14,32],"$n$th":[16],"roots":[17],"of":[18,47,82,104,117,124,127,135,144],"unity.":[19],"Based":[20],"on":[21,92,100],"these":[22,111,145],"data,":[23],"how":[24,110],"can":[25,40],"we":[26,41,131],"approximately":[27],"evaluate":[28],"$f^{(m)}(z)$":[31],"a":[33,125],"point":[34],"$z$":[35],"disk?":[38,51],"How":[39],"calculate":[42],"zeros":[44],"poles":[46],"$f$":[48],"These":[52],"questions":[53],"exhibit":[54],"purest":[57],"form":[58],"certain":[59],"algorithmic":[60],"issues":[61],"that":[62],"arise":[63],"across":[64],"computational":[65],"science":[66],"areas":[68],"including":[69],"integral":[70],"equations,":[71,74],"partial":[72],"differential":[73],"and":[75,85,97],"large-scale":[76],"linear":[77],"algebra.":[78],"We":[79,107],"analyze":[80],"some":[81,143],"possibilities":[84],"emphasize":[86],"distinction":[88],"between":[89],"algorithms":[90],"based":[91,99],"polynomial":[93,140],"rational":[95,136],"interpolation":[96],"those":[98],"trapezoidal":[101],"rule":[102],"approximations":[103,141],"Cauchy":[105],"integrals.":[106],"then":[108],"show":[109],"developments":[112],"apply":[113],"to":[114],"problem":[116],"computing":[118],"eigenvalues":[120],"matrix":[126],"large":[128],"dimension.":[129],"Finally":[130],"highlight":[132],"power":[134],"comparison":[138],"with":[139],"for":[142],"problems.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
