Numerical Stability of Fast Trigonometric Transforms – A Worst Case Study
نویسندگان
چکیده
This paper presents some new results on numerical stability for various fast trigonometric transforms. In a worst case study, we consider the numerical stability of the classical fast Fourier transform (FFT) with respect to different precomputation methods for the involved twiddle factors and show the strong influence of precomputation errors on the numerical stability of the FFT. The examinations are extended to fast algorithms for the computation of discrete cosine and sine transforms and to efficient computations of discrete Fourier transforms for nonequispaced data. Numerical tests confirm the theoretical estimates of numerical stability. ∗ Contact author: Manfred Tasche, Mailing address: Department of Mathematics,University of Rostock,D – 18051 Rostock, Germany, Tel. 0049 / 381 – 498 – 1549, Fax 0049 / 381 – 498 – 1520, e–mail: [email protected]
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