Fast Fourier Transforms for Nonequispaced Data, II
نویسندگان
چکیده
منابع مشابه
Fast Fourier Transforms for Nonequispaced Data
A group of algorithms is presented generalizing the fast Fourier transform to the case of nonin-teger frequencies and nonequispaced nodes on the interval [-r, r]. The schemes of this paper are based on a combination of certain analytical considerations with the classical fast Fourier transform and generalize both the forward and backward FFTs. Each of the algorithms requires O(N log N + N-log(I...
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In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequi-spaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFT{algorithms with respect to roundoo errors and...
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This paper presents some new results on numerical stability for multivariate fast Fourier transform of nonequispaced data (NFFT). In contrast to fast Fourier transform (of equispaced data), the NFFT is an approximate algorithm. In a worst case study, we show that both approximation error and roundoff error have a strong influence on the numerical stability of NFFT. Numerical tests confirm the t...
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The fast calculation of long-range interactions is a demanding problem in particle simulation. The main focus of our approach is the decomposition of the problem in building blocks and present efficient numerical realizations for these blocks. For that reason we recapitulate the fast Fourier transform at nonequispaced nodes and the fast summation method. We describe the application of these alg...
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A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like the fast Fourier transform (FFT) have high computational costs. Hyperbolic cross approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivati...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 1995
ISSN: 1063-5203
DOI: 10.1006/acha.1995.1007