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Fast and approximate computation of Laplace and Fourier transforms

Ines Melzer
ISBN 978-3-8325-4226-9
125 Seiten, Erscheinungsjahr: 2016
Preis: 34.00 EUR

Inhaltsverzeichnis (PDF)

Stichworte/keywords: fast Laplace transform, fast Fourier transform, nonharmonic Fourier series, real and complex exponential sums, trigonometric approximation

In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments.

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