title:
Stable reconstruction of hyperbolic cross trigonometric polynomials from samples of generated sets 
name:
Kaemmerer 
first name:
Lutz

location/conference:
SPPJT11

PRESENTATIONlink:
http://www.dfgspp1324.de/nuhagtools/event_NEW/dateien/SPPJT11/talks/SPPJT2011_02_kaemmerer.pdf 
abstract:
Trigonometric polynomials with frequencies only supported by hyperbolic crosses allow for a
good approximation of functions of appropriate smoothness and decrease
the number of used Fourier coefficients strongly.
Sparse grids are the natural discretisations in the spatial domain. The corresponding Fourier transform suffers from stability problems. For that reason we consider sets produced by multiples of a socalled generating vector as spatial discretisations, a generalisation of rank1 lattices. Applying a onedimensional NFFT, an easy and fast evaluation of trigonometric polynomials at the grid nodes is guaranteed. Some additional assumptions ensure even stability and besides the fast reconstruction of trigonometric polynomials from the function values. 