Error Analysis of Some Operations Involved in the Cooley-Tukey Fast Fourier Transform

被引：11
|
作者：
Brisebarre, Nicolas [1 ,5 ]
Joldes, Mioara [2 ]
Muller, Jean-Michel [1 ,5 ]
Nanes, Ana-Maria [3 ]
Picot, Joris [4 ,5 ]
机构：
[1] Univ Lyon, LIP, CNRS, Lyon, France
[2] CNRS, LAAS, 7 Ave Colonel Roche, F-31077 Toulouse 7, France
[3] Tech Univ Cluj Napoca, Cluj Napoca 400114, Romania
[4] Univ Lyon, LIP, ENS Lyon, Lyon, France
[5] ENS Lyon, LIP, 46 Allee Italie, F-69364 Lyon 07, France
来源：
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | 2020年 / 46卷 / 02期
关键词：
Floating-point arithmetic; fast Fourier transform; rounding error analysis; MULTIPLICATION; ALGORITHM;
D O I：
10.1145/3368619
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We are interested in obtaining error bounds for the classical Cooley-Tukey fast Fourier transform algorithm in floating-point arithmetic, for the 2-norm as well as for the infinity norm. 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 x, assuming that all terms of x have real and imaginary parts less than some value b.
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收藏
页数：27
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