Abstract
Many problems in applied and computational analysis require the evaluation of the (discrete) Fourier transform of a sequence of complex numbers with period n. While straightforward evaluation of the transform requires n2 multiplications and additions, the fast Fourier transform (FFT) algorithm of Cooley and Tukey achieves the same goal using only n log2n such operations. Two applications of this algorithm are indicated: a) The Theodorsen method in numerical conformai mapping, where using FFT one iteration costs only O(nlog2n) operations in place of the O(n2) operations required by the Wittich method; b) computations with formal power series, where using FFT the first n coefficients of products, quotients, and square roots can be obtained in O(n log2n) operations.
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Henrici, P. (1976). Einige Anwendungen der Schnellen Fouriertransformation. In: Albrecht, J., Collatz, L. (eds) Moderne Methoden der Numerischen Mathematik. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 32. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5501-3_8
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DOI: https://doi.org/10.1007/978-3-0348-5501-3_8
Publisher Name: Birkhäuser, Basel
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