Fast and approximate computation of Laplace and Fourier transforms

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Title: Fast and approximate computation of Laplace and Fourier transforms
Other Titles: Schnelle und approximative Berechnung von Laplace- und Fourier-Transformationen
Authors: Melzer, Ines
Abstract: 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.
Citations: Dissertation. Universität Osnabrück, 2016. Berlin, Logos Verlag, 2016
ISBN: 978-3-8325-4226-9
Subject Keywords: fast Laplace transform; fast Fourier transform; nonharmonic Fourier series; real and complex exponential sums; trigonometric approximation
Issue Date: 4-Apr-2016
License name: Namensnennung-NichtKommerziell-KeineBearbeitung 3.0 Unported
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Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - Hochschulschriften

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