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Algorithms for unequally spaced fast Laplace transforms

Andersson, Fredrik LU (2013) In Applied and Computational Harmonic Analysis 35(3). p.419-432
Abstract
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.... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Discrete Laplace transforms, Fast algorithms, USFFT, Fast application of complex Vandermonde matrices
in
Applied and Computational Harmonic Analysis
volume
35
issue
3
pages
419 - 432
publisher
Elsevier
external identifiers
  • wos:000324848400004
  • scopus:84883859082
ISSN
1096-603X
DOI
10.1016/j.acha.2012.11.005
language
English
LU publication?
yes
id
aaa3c2f5-ba77-43a8-84cc-043041c5ea46 (old id 3358138)
date added to LUP
2016-04-01 10:44:48
date last changed
2022-02-17 20:55:01
@article{aaa3c2f5-ba77-43a8-84cc-043041c5ea46,
  abstract     = {{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.}},
  author       = {{Andersson, Fredrik}},
  issn         = {{1096-603X}},
  keywords     = {{Discrete Laplace transforms; Fast algorithms; USFFT; Fast application of complex Vandermonde matrices}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{419--432}},
  publisher    = {{Elsevier}},
  series       = {{Applied and Computational Harmonic Analysis}},
  title        = {{Algorithms for unequally spaced fast Laplace transforms}},
  url          = {{http://dx.doi.org/10.1016/j.acha.2012.11.005}},
  doi          = {{10.1016/j.acha.2012.11.005}},
  volume       = {{35}},
  year         = {{2013}},
}