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Association for Computing Machinery (ACM), ACM Transactions on Mathematical Software, 2(46), p. 1-27, 2020

DOI: 10.1145/3368619



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

This paper is available in a repository.
This paper is available in a repository.

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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 .