Fast and approximate computation of Laplace and Fourier transforms
Author | : Ines Melzer |
Publisher | : Logos Verlag Berlin GmbH |
Total Pages | : 126 |
Release | : 2016-03-20 |
ISBN-10 | : 9783832542269 |
ISBN-13 | : 3832542264 |
Rating | : 4/5 (69 Downloads) |
Download or read book Fast and approximate computation of Laplace and Fourier transforms written by Ines Melzer and published by Logos Verlag Berlin GmbH. This book was released on 2016-03-20 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.