Numerical stability of nonequispaced fast Fourier transforms

被引：14
|
作者：
Potts, Daniel [1 ]
Tasche, Manfred [2 ]
机构：
[1] Tech Univ Chemnitz, Dept Math, D-09107 Chemnitz, Germany
[2] Univ Rostock, Inst Math, D-18051 Rostock, Germany
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2008年 / 222卷 / 02期
关键词：
Fast Fourier transform; Nonequispaced data; Nonequispaced FFT; Numerical stability; Roundoff error; Approximation error; Sampling of trigonometric polynomials;
D O I：
10.1016/j.cam.2007.12.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents some new results Oil numerical stability for multivariate fast Fourier transform of no nonequispaced data (NFFT). In contrast to last Fourier transform (of equispaced data), the NFFT is all approximate algorithm. In a worst case study, we show that both approximation error and roundoff error have I strong influence Oil the numerical stability of NFFT. Numerical tests confirm the theoretical estimates of numerical stability. (C) 2007 Elsevier B.V All rights reserved.
引用
收藏
页码：655 / 674
页数：20
相关论文
共 50 条
  • [1] A note on fast Fourier transforms for nonequispaced grids
    Steidl, G
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 1998, 9 (3-4) : 337 - 352
  • [2] A note on fast Fourier transforms for nonequispaced grids
    Gabriele Steidl
    Advances in Computational Mathematics, 1998, 9 : 337 - 352
  • [3] FAST FOURIER-TRANSFORMS FOR NONEQUISPACED DATA
    DUTT, A
    ROKHLIN, V
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1993, 14 (06) : 1368 - 1393
  • [4] NONEQUISPACED HYPERBOLIC CROSS FAST FOURIER TRANSFORM
    Doehler, Michael
    Kunis, Stefan
    Potts, Daniel
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 47 (06) : 4415 - 4428
  • [5] Numerical stability of fast cosine transforms
    Baszenski, G
    Schreiber, U
    Tasche, M
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2000, 21 (1-2) : 25 - 46
  • [6] Numerical Accuracy of Fast Fourier Transforms with CORDIC Arithmetic
    M. Bekooij
    J. Huisken
    K. Nowak
    Journal of VLSI signal processing systems for signal, image and video technology, 2000, 25 : 187 - 193
  • [7] Numerical accuracy of fast Fourier transforms with CORDIC arithmetic
    Bekooij, M
    Huisken, J
    Nowak, K
    JOURNAL OF VLSI SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY, 2000, 25 (02): : 187 - 193
  • [8] A FAST METHOD FOR THE NUMERICAL EVALUATION OF CONTINUOUS FOURIER AND LAPLACE TRANSFORMS
    BAILEY, DH
    SWARZTRAUBER, PN
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1994, 15 (05) : 1105 - 1110
  • [9] Multidimensional Fourier Interpolation and Fast Fourier Transforms
    Basalov, Yu. A.
    Dobrovolsky, N. N.
    Chubarikov, V. N.
    DOKLADY MATHEMATICS, 2024, 109 (03) : 224 - 226
  • [10] FAST COMPUTATION OF PARTIAL FOURIER TRANSFORMS
    Ying, Lexing
    Fomel, Sergey
    MULTISCALE MODELING & SIMULATION, 2009, 8 (01) : 110 - 124
12345