Fast evaluation of real and complex exponential sums

Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we propose a certain fast Fourier-Laplace transform, which in parti...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2016-06
Main Authors: Kunis, Stefan, Melzer, Ines
Format: Article
Language:English
Subjects:
Integral transforms
Laplace transforms
Mathematical analysis
Polynomials
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we propose a certain fast Fourier-Laplace transform, which in particular allows for the fast evaluation of polynomials at nodes in the complex unit disk. All theoretical results are illustrated by numerical experiments.
ISSN:2331-8422