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title:
Reconstructing multivariate trigonometric polynomials by sampling along generated sets |
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name:
Kaemmerer |
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first name:
Lutz
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location/conference:
SPP-JT12
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event_NEW/dateien/SPP-JT12/talks/Kaemmerer-jt12.pdf |
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abstract:
The approximation of problems in $d$ spatial dimensions by sparse trigonometric polynomials supported on known or unknown frequency sets $I\subset\mathbb{Z}^d$ is an important task with a variety of applications.
The use of a generalisation of rank-1 lattices as spatial discretisations offers a suitable possibility for sampling such sparse trigonometric polynomials.
We assume the knowledge of the frequency set $I\subset\mathbb{Z}^d$ and construct corresponding sampling sets that allow a stable and unique discrete Fourier transform.
A multivariate trigonometric polynomial evaluated at all nodes of these sampling sets essentially simplifies to a one-dimensional nonequispaced discrete Fourier transform of the length of the number of used sampling nodes.
Applying the one-dimensional nonequispaced fast Fourier transform enables the fast evaluation and reconstruction of the multivariate trigonometric polynomials. |
