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Algorithms for unequally spaced fast Laplace transforms

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Author

  • Fredrik Andersson

Summary, in English

Fast algorithms for unequally spaced discrete Laplace transforms are presented. The algorithms are approximate up to a prescribed choice of computational precision, and they employ modified versions of algorithms for unequally spaced fast Fourier transforms using Gaussians. Various configurations of sums with equally and unequally spaced points can be dealt with. In contrast to previously presented fast algorithms for fast discrete Laplace transforms, the proposed algorithms are not restricted to the case of real exponentials but can deal with oscillations caused by complex valued nodes. Numerical experiments show that the computational complexity is comparable to that of computing ordinary discrete Fourier transforms by means of FFT. Results are given for the one-dimensional case, but it is straightforward to generalize them to arbitrary dimensions.

Publishing year

2013

Language

English

Pages

419-432

Publication/Series

Applied and Computational Harmonic Analysis

Volume

35

Issue

3

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Discrete Laplace transforms
  • Fast algorithms
  • USFFT
  • Fast application of complex Vandermonde matrices

Status

Published

Research group

  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 1096-603X