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.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:repositorium.ub.uni-osnabrueck.de:urn:nbn:de:gbv:700-2016040414362 |
| Date | 04 April 2016 |
| Creators | Melzer, Ines |
| Source Sets | Universität Osnabrück |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
| Rights | Namensnennung-NichtKommerziell-KeineBearbeitung 3.0 Unported, http://creativecommons.org/licenses/by-nc-nd/3.0/ |
| Relation | http://www.logos-verlag.de/cgi-bin/buch/isbn/4226 |
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