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Please use this identifier to cite or link to this item: urn:nbn:de:gbv:700-2016040414362

Title: Fast and approximate computation of Laplace and Fourier transforms
Other Titles: Schnelle und approximative Berechnung von Laplace- und Fourier-Transformationen
Author(s): 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.
Issue Date: 2016-04-04T08:42:54Z
Date of oral examination: 2016
Appears in Collections:FB06 - Hochschulschriften

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