{"id":"https://openalex.org/W2055689533","doi":"https://doi.org/10.1137/130921544","title":"A Parallel Butterfly Algorithm","display_name":"A Parallel Butterfly Algorithm","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2055689533","doi":"https://doi.org/10.1137/130921544","mag":"2055689533"},"language":"en","primary_location":{"id":"doi:10.1137/130921544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921544","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/88176","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030891646","display_name":"Jack Poulson","orcid":"https://orcid.org/0000-0002-5435-2883"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jack Poulson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035951153","display_name":"Laurent Demanet","orcid":"https://orcid.org/0000-0001-7052-5097"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laurent Demanet","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028352097","display_name":"Nicholas Maxwell","orcid":"https://orcid.org/0000-0002-2575-5990"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicholas Maxwell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011918131","display_name":"Lexing Ying","orcid":"https://orcid.org/0000-0003-1547-1457"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lexing Ying","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030891646"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4865,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.92831633,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"36","issue":"1","first_page":"C49","last_page":"C65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9984999895095825,"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":0.9984999895095825,"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/T11946","display_name":"Antenna Design and Optimization","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12450","display_name":"Radio Astronomy Observations and Technology","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6219834089279175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5630152225494385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46283864974975586},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.46177470684051514},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.44779539108276367},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.445309042930603},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2662930190563202}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6219834089279175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5630152225494385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46283864974975586},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.46177470684051514},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.44779539108276367},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.445309042930603},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2662930190563202}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130921544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921544","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:10.1.1.744.8968","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.744.8968","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1305.4650.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/88176","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/88176","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Society for Industrial and Applied Mathematics","raw_type":"http://purl.org/eprint/type/JournalArticle"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/597370","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/597370","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"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":{"id":"pmh:oai:dspace.mit.edu:1721.1/88176","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/88176","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Society for Industrial and Applied Mathematics","raw_type":"http://purl.org/eprint/type/JournalArticle"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1508603278","https://openalex.org/W1982811641","https://openalex.org/W1986681927","https://openalex.org/W1987551888","https://openalex.org/W1994148398","https://openalex.org/W2002199481","https://openalex.org/W2008205484","https://openalex.org/W2018743852","https://openalex.org/W2026283299","https://openalex.org/W2030815520","https://openalex.org/W2038019732","https://openalex.org/W2041351581","https://openalex.org/W2059300917","https://openalex.org/W2063399239","https://openalex.org/W2083206954","https://openalex.org/W2087995885","https://openalex.org/W2089210221","https://openalex.org/W2093529653","https://openalex.org/W2102061396","https://openalex.org/W2104373803","https://openalex.org/W2105111377","https://openalex.org/W2105549957","https://openalex.org/W2117762537","https://openalex.org/W2119233169","https://openalex.org/W2131613942","https://openalex.org/W2138950524","https://openalex.org/W2140157092","https://openalex.org/W2140980608","https://openalex.org/W2143962756","https://openalex.org/W2152356156","https://openalex.org/W2156722294","https://openalex.org/W2170796499","https://openalex.org/W2569750427","https://openalex.org/W3100417409","https://openalex.org/W4213311204","https://openalex.org/W4233363368","https://openalex.org/W4301871668"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W141820298","https://openalex.org/W4378770497","https://openalex.org/W2049584446","https://openalex.org/W2544423928","https://openalex.org/W2079781215","https://openalex.org/W2064404759","https://openalex.org/W4308245303","https://openalex.org/W4389519396"],"abstract_inverted_index":{"The":[0],"butterfly":[1,81],"algorithm":[2,6,69,82,116],"is":[3,31,61,70,83,137],"a":[4,10,39,87,138,169],"fast":[5],"which":[7],"approximately":[8,32,62],"evaluates":[9],"discrete":[11],"analogue":[12,167],"of":[13,24,59,67,79,90,96,123,156,168],"the":[14,28,64,68,80,121,124,129],"integral":[15],"transform":[16,173],"$\\int_{\\mathbb{R}^d}":[17],"K(x,y)":[18],"g(y)":[19],"dy$":[20],"at":[21,71,100],"large":[22],"numbers":[23],"target":[25,53],"points":[26],"when":[27,34,55],"kernel,":[29],"$K(x,y)$,":[30],"low-rank":[33],"restricted":[35],"to":[36,177,182],"subdomains":[37],"satisfying":[38],"certain":[40],"simple":[41],"geometric":[42],"condition.":[43],"In":[44],"$d$":[45],"dimensions":[46],"with":[47,184],"$O(N^d)$":[48],"quasi-uniformly":[49],"distributed":[50],"source":[51],"and":[52,92,165,188],"points,":[54],"each":[56],"appropriate":[57],"submatrix":[58],"$K$":[60],"rank-$r$,":[63],"running":[65],"time":[66,110],"most":[72,101],"$O(r^2":[73,102],"N^d":[74],"\\log":[75,104],"N)$.":[76],"A":[77],"parallelization":[78],"introduced":[84],"which,":[85],"assuming":[86],"message":[88],"latency":[89],"$\\alpha$":[91],"per-process":[93],"inverse":[94],"bandwidth":[95],"$\\beta$,":[97],"executes":[98],"in":[99,120],"\\frac{N^d}{p}":[103],"N":[105],"+":[106],"(\\beta":[107],"r\\frac{N^d}{p}+\\alpha)\\log":[108],"p)$":[109],"using":[111],"$p$":[112],"processes.":[113],"This":[114],"parallel":[115],"was":[117],"then":[118],"instantiated":[119],"form":[122],"open-source":[125],"\\textttDistButterfly":[126],"library":[127],"for":[128,153],"special":[130],"case":[131],"where":[132,135],"$K(x,y)=\\exp(i":[133],"\\Phi(x,y))$,":[134],"$\\Phi(x,y)$":[136],"black-box,":[139],"sufficiently":[140],"smooth,":[141],"real-valued":[142],"phase":[143,157],"function.":[144],"Experiments":[145],"on":[146],"Blue":[147],"Gene/Q":[148],"demonstrate":[149],"impressive":[150],"strong-scaling":[151],"results":[152],"important":[154],"classes":[155],"functions.":[158],"Using":[159],"quasi-uniform":[160],"sources,":[161],"hyperbolic":[162],"Radon":[163,172],"transforms,":[164],"an":[166],"three-dimensional":[170],"generalized":[171],"were,":[174],"respectively,":[175],"observed":[176],"strong-scale":[178],"from":[179],"1-node/16-cores":[180],"up":[181],"1024-nodes/16,384-cores":[183],"greater":[185],"than":[186],"90%":[187],"82%":[189],"efficiency,":[190],"respectively.":[191]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}