Error Analysis of Some Operations Involved in the Cooley-Tukey Fast Fourier Transform
Nicolas Brisebarre, Mioara Joldeş, Jean‐Michel Muller, Ana-Maria Naneş, Joris Picot · ACM Transactions on Mathematical Software · 2020
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 .