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
URL:	https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016040414362
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
License url:	http://creativecommons.org/licenses/by-nc-nd/3.0/
Type of publication:	Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:	FB06 - Hochschulschriften

This item is licensed under a Creative Commons License