Cooley-Tukey快速傅里叶变换中一些运算的误差分析

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2020-05-18 DOI:10.1145/3368619

N. Brisebarre, Mioara Joldes, J. Muller, Ana-Maria Naneş, Joris Picot

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引用次数: 14

摘要

我们感兴趣的是获得经典的Cooley-Tukey快速傅立叶变换算法在浮点运算中的误差界，对于2范数以及对于无穷范数。为了这个目的，我们也给出了一些结果关于复数乘以一个单位根的相对误差，以及关于向量x的快速傅里叶变换的一项的实部或虚部的最大值，假设x的所有项的实部和虚部都小于某个值b。

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

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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ACM Transactions on Mathematical Software (TOMS)

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