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

Author:

Brisebarre Nicolas1,Joldeş Mioara2,Muller Jean-Michel3ORCID,Naneş Ana-Maria4,Picot Joris5

Affiliation:

1. CNRS, LIP, Université de Lyon

2. CNRS, LAAS, Toulouse, Toulouse, Cedex, France

3. CNRS, LIP, Université de Lyon, Lyon Cedex, France

4. Technical University of Cluj-Napoca, Cluj-Napoca, Romania

5. ENS de Lyon, LIP, Université de Lyon, Lyon Cedex, France

Abstract

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 .

Funder

FastRelax grant of the French Agence Nationale de la Recherche

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Precision Loss in Approximate Homomorphic Encryption;Lecture Notes in Computer Science;2024

2. Quantum-Safe HIBE: Does It Cost a Latte?;IEEE Transactions on Information Forensics and Security;2024

3. Efficient and Validated Numerical Evaluation of Abelian Integrals;ACM Transactions on Mathematical Software;2023-12-18

4. Testing the Sharpness of Known Error Bounds on the Fast Fourier Transform;2023 IEEE 30th Symposium on Computer Arithmetic (ARITH);2023-09-04

5. TurboStencil: You only compute once for stencil computation;Future Generation Computer Systems;2023-09

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3