Fast and Approximate Computation of Laplace and Fourier Transforms - Couverture souple

Melzer, Ines

9783832542269: Fast and Approximate Computation of Laplace and Fourier Transforms

Couverture souple

ISBN 10 : 3832542264 ISBN 13 : 9783832542269

Editeur : Logos Verlag Berlin GmbH, 2016

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^TFast and Approximate Computation of Laplace and Fourier Transforms ^Aby Ines Melzer ^DIn 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.

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