Fast and approximate computation of Laplace and Fourier transforms

Ines Melzer

ISBN 978-3-8325-4226-9
125 pages, year of publication: 2016
price: 34.00 €
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.

Table of contents (PDF)


  • fast Laplace transform
  • fast Fourier transform
  • nonharmonic Fourier series
  • real and complex exponential sums
  • trigonometric approximation

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