Error analysis of some operations involved in the Cooley-Tukey Fast Fourier Transform - Archive ouverte HAL Access content directly
Journal Articles ACM Transactions on Mathematical Software Year : 2020

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

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 $b$.
Fichier principal
Vignette du fichier
Bounds-FFT-HaLV2-oct19.pdf (618.68 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01949458 , version 1 (10-12-2018)
hal-01949458 , version 2 (23-10-2019)

Identifiers

Cite

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, 2020, 46 (2), pp.1-34. ⟨10.1145/3368619⟩. ⟨hal-01949458v2⟩
674 View
1529 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More