Geodesic
Fast evaluation of real and complex exponential sums
Electronic transactions on numerical analysis, Tome 46 (2017), pp. 23-35
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory or 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.
Classification : 65T50, 42A15, 30E10, 65D05, 65F30
Keywords: trigonometric approximation, nonharmonic Fourier series, fast Fourier transform, integral transforms, hierarchical matrices 
@article{ETNA_2017__46__a12,
     author = {Kunis,  Stefan and Melzer,  Ines},
     title = {Fast evaluation of real and complex exponential sums},
     journal = {Electronic transactions on numerical analysis},
     pages = {23--35},
     year = {2017},
     volume = {46},
     zbl = {1355.65187},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2017__46__a12/}
}
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AU  - Melzer,  Ines
TI  - Fast evaluation of real and complex exponential sums
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VL  - 46
UR  - http://geodesic.mathdoc.fr/item/ETNA_2017__46__a12/
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%A Melzer,  Ines
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%J Electronic transactions on numerical analysis
%D 2017
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%U http://geodesic.mathdoc.fr/item/ETNA_2017__46__a12/
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%F ETNA_2017__46__a12
Kunis,  Stefan; Melzer,  Ines. Fast evaluation of real and complex exponential sums. Electronic transactions on numerical analysis, Tome 46 (2017), pp. 23-35. http://geodesic.mathdoc.fr/item/ETNA_2017__46__a12/