{"id":"https://openalex.org/W2029304625","doi":"https://doi.org/10.1137/0911007","title":"Analytic Continuation by the Fast Fourier Transform","display_name":"Analytic Continuation by the Fast Fourier Transform","publication_year":1990,"publication_date":"1990-01-01","ids":{"openalex":"https://openalex.org/W2029304625","doi":"https://doi.org/10.1137/0911007","mag":"2029304625"},"language":"en","primary_location":{"id":"doi:10.1137/0911007","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0911007","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical 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/A5032096798","display_name":"Joel Franklin","orcid":"https://orcid.org/0000-0002-9073-5507"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joel Franklin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032096798"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.16242525,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"1","first_page":"112","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9965999722480774,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9965999722480774,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9948999881744385,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9929999709129333,"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/hadamard-transform","display_name":"Hadamard transform","score":0.758179783821106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7096860408782959},{"id":"https://openalex.org/keywords/analytic-continuation","display_name":"Analytic continuation","score":0.6608147621154785},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.5894022583961487},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5657095313072205},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5219357013702393},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5050502419471741},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4860951900482178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47532203793525696},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4396735727787018},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.4163912534713745},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4036412239074707},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.32923799753189087},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.23204201459884644},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15045028924942017}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.758179783821106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7096860408782959},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.6608147621154785},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5894022583961487},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5657095313072205},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5219357013702393},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5050502419471741},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4860951900482178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47532203793525696},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4396735727787018},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.4163912534713745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4036412239074707},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.32923799753189087},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.23204201459884644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15045028924942017},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0911007","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0911007","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical Computing","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:4869","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/4869/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1036732791","https://openalex.org/W1965140665","https://openalex.org/W1970409224","https://openalex.org/W2000209770","https://openalex.org/W2007701489","https://openalex.org/W2039596515","https://openalex.org/W2042461256","https://openalex.org/W2044659220","https://openalex.org/W2061171222","https://openalex.org/W2066034539","https://openalex.org/W2149846618","https://openalex.org/W2160615443","https://openalex.org/W2329563144","https://openalex.org/W2483864909","https://openalex.org/W2563315642","https://openalex.org/W4206411922"],"related_works":["https://openalex.org/W2025238519","https://openalex.org/W4251351562","https://openalex.org/W2769742667","https://openalex.org/W2233343535","https://openalex.org/W2019980603","https://openalex.org/W2179391051","https://openalex.org/W4379386706","https://openalex.org/W2081296308","https://openalex.org/W1996192395","https://openalex.org/W2074194659"],"abstract_inverted_index":{"The":[0,26],"ill-posed":[1],"problem":[2],"of":[3,45,68],"analytic":[4],"continuation":[5],"is":[6,16,19,56],"regularized":[7],"by":[8,64],"a":[9,33,43],"prescribed":[10,51,63],"bound.":[11],"A":[12],"simple":[13],"computer":[14],"algorithm":[15,27],"given":[17],"that":[18,62],"based":[20],"on":[21],"the":[22,46,50,53,65],"fast":[23],"Fourier":[24],"transform.":[25],"computes":[28],"m":[29],"complex":[30],"values":[31],"and":[32,49],"positive":[34],"error":[35,55],"bound":[36],"with":[37,61],"time":[38],"complexity":[39],"$O(m\\log":[40],"m)$.":[41],"As":[42],"function":[44],"data":[47],"errors":[48],"bound,":[52],"numerical":[54],"shown":[57],"to":[58],"be":[59],"consistent":[60],"three-circles":[66],"principle":[67],"Hadamard.":[69]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}