Error analysis of some operations involved in the Cooley-Tukey Fast Fourier Transform
Résumé
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 $b$.
Mots clés
Numeric approximation algorithms
• Theory of computation → Design and analysis of algorithms
Rounding error analysis ACM Reference format:
Floating-point arithmetic
CCS Concepts: • Mathematics of computing → Mathematical software
Rounding error analysis
Additional Key Words and Phrases: Floating-point arithmetic
Fast Fourier Transform
| Origine | Fichiers produits par l'(les) auteur(s) |
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