{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:22:11Z","timestamp":1787383331348,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DTRA-DMS 1322393"],"award-info":[{"award-number":["DTRA-DMS 1322393"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["RG160236"],"award-info":[{"award-number":["RG160236"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-AC02-06CH11357"],"award-info":[{"award-number":["DE-AC02-06CH11357"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. The complexity of the algorithm is $\\mathcal{O}\\bigl(N (\\log N)^2\\bigr)$, where $N$ is the number of degrees of freedom used in each of the Fourier extensions.<\/jats:p>","DOI":"10.1137\/17m1114764","type":"journal-article","created":{"date-parts":[[2017,12,21]],"date-time":"2017-12-21T11:36:41Z","timestamp":1513856201000},"page":"A3089-A3106","source":"Crossref","is-referenced-by-count":7,"title":["A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions"],"prefix":"10.1137","volume":"39","author":[{"given":"Kuan","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony P.","family":"Austin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ke","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,12,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.09.069"},{"key":"atypb2","volume-title":"Frames and Numerical Approximation, preprint https:\/\/arxiv.org\/abs\/1612.04464v2 [math.NA]","author":"Adcock B.","year":"2017"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-013-9158-8"},{"key":"atypb4","volume-title":"Optimal Sampling Rates for Approximating Analytic Functions from Pointwise Samples, preprint https:\/\/arxiv.org\/abs\/1610.04769v2 [math.NA]","author":"Adcock B.","year":"2017"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.05.036"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626340"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7023"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.12.087"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543234"},{"key":"atypb10","volume-title":"The Numerical Solution of Volterra Equations","author":"Brunner H.","year":"1986"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.08.029"},{"key":"atypb12","volume-title":"Chebfun Guide","author":"Driscoll T. A.","year":"2014"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177731708"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/140955835"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/090752456"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/11082436X"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/15M1030923"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/090774707"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2007.165.55"},{"key":"atypb20","volume-title":"Approximation Theory and Approximation Practice","author":"Trefethen L. N.","year":"2013"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970999"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1114764","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:39:26Z","timestamp":1787333966000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1114764"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/17M1114764"],"URL":"https:\/\/doi.org\/10.1137\/17m1114764","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}