Error analysis of some operations involved in the Cooley-Tukey Fast Fourier Transform

Nicolas Brisebarre 1, 2 Mioara Joldes 3, 2 Jean-Michel Muller 1, 2 Ana-Maria Naneş 4 Joris Picot 1
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : We are interested in obtaining error bounds for the classical Cooley-Tukey FFT 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 FFT of a vector $x$, assuming that all terms of $x$ have real and imaginary parts less than some value $b$.
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Nicolas Brisebarre, Mioara Joldes, Jean-Michel Muller, Ana-Maria Naneş, Joris Picot. Error analysis of some operations involved in the Cooley-Tukey Fast Fourier Transform. ACM Transactions on Mathematical Software, Association for Computing Machinery, In press, pp.1-34. ⟨10.1145/nnnnnnn.nnnnnnn⟩. ⟨hal-01949458v2⟩

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