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Fast and approximate computation of Laplace and Fourier transforms

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016040414362
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dc.creatorMelzer, Ines
dc.date.accessioned2016-04-04T08:42:54Z
dc.date.available2016-04-04T08:42:54Z
dc.date.issued2016-04-04T08:42:54Z
dc.identifier.citationDissertation. Universität Osnabrück, 2016. Berlin, Logos Verlag, 2016
dc.identifier.isbn978-3-8325-4226-9
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016040414362-
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.relationhttp://www.logos-verlag.de/cgi-bin/buch/isbn/4226
dc.rightsNamensnennung-NichtKommerziell-KeineBearbeitung 3.0 Unported-
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/-
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.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2016-
dc.subject.msc42-04 - Explicit machine computation and programs
dc.subject.msc65-02 - Research exposition
vCard.ORGFB6
Appears in Collections:FB06 - Hochschulschriften

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