Fast and approximate computation of Laplace and Fourier transforms

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dc.creatorMelzer, Ines
dc.identifier.citationDissertation. Universität Osnabrück, 2016. Berlin, Logos Verlag, 2016
dc.description.abstractIn 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.eng
dc.rightsNamensnennung-NichtKommerziell-KeineBearbeitung 3.0 Unported-
dc.subjectfast Laplace transformeng
dc.subjectfast Fourier transformeng
dc.subjectnonharmonic Fourier serieseng
dc.subjectreal and complex exponential sumseng
dc.subjecttrigonometric approximationeng
dc.subject.ddc510 - Mathematik
dc.titleFast and approximate computation of Laplace and Fourier transformseng
dc.title.alternativeSchnelle und approximative Berechnung von Laplace- und Fourier-Transformationenger
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.typeDissertation [thesis.doctoral]-
dc.subject.msc42-04 - Explicit machine computation and programs
dc.subject.msc65-02 - Research exposition
Appears in Collections:FB06 - Hochschulschriften

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