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For that purpose, we also give some results on the relative error of the complex multiplication by a root of unity, and on the largest value that can take the real or imaginary part of one term of the fast Fourier transform of a vector\n            <jats:italic>x<\/jats:italic>\n            , assuming that all terms of\n            <jats:italic>x<\/jats:italic>\n            have real and imaginary parts less than some value\n            <jats:italic>b<\/jats:italic>\n            .\n          <\/jats:p>","DOI":"10.1145\/3368619","type":"journal-article","created":{"date-parts":[[2020,5,22]],"date-time":"2020-05-22T23:58:23Z","timestamp":1590191903000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Error Analysis of Some Operations Involved in the Cooley-Tukey Fast Fourier Transform"],"prefix":"10.1145","volume":"46","author":[{"given":"Nicolas","family":"Brisebarre","sequence":"first","affiliation":[{"name":"CNRS, LIP, Universit\u00e9 de Lyon"}]},{"given":"Mioara","family":"Jolde\u015f","sequence":"additional","affiliation":[{"name":"CNRS, LAAS, Toulouse, Toulouse, Cedex, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3588-0047","authenticated-orcid":false,"given":"Jean-Michel","family":"Muller","sequence":"additional","affiliation":[{"name":"CNRS, LIP, Universit\u00e9 de Lyon, Lyon Cedex, France"}]},{"given":"Ana-Maria","family":"Nane\u015f","sequence":"additional","affiliation":[{"name":"Technical University of Cluj-Napoca, Cluj-Napoca, Romania"}]},{"given":"Joris","family":"Picot","sequence":"additional","affiliation":[{"name":"ENS de Lyon, LIP, Universit\u00e9 de Lyon, Lyon Cedex, France"}]}],"member":"320","published-online":{"date-parts":[[2020,5,19]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7087"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-01931-X"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1991-1068824-0"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1965-0178586-1"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(90)90158-U"},{"volume-title":"Proceedings of the Fall Joint Computer Conference. 563--578","author":"Gentleman W.","key":"e_1_2_1_6_1","unstructured":"W. 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