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SIAMNUM
2010

Nonequispaced Hyperbolic Cross Fast Fourier Transform

12 years 9 months ago
Nonequispaced Hyperbolic Cross Fast Fourier Transform
A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like the fast Fourier transform (FFT) have high computational costs. Hyperbolic cross approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivatives. We propose a nonequispaced hyperbolic cross fast Fourier transform based on one hyperbolic cross FFT and a dedicated interpolation by splines on sparse grids. Analogously to the nonequispaced FFT for trigonometric polynomials with Fourier coefficients supported on the full grid, this allows for the efficient evaluation of trigonometric polynomials with Fourier coefficients supported on the hyperbolic cross at arbitrary spatial sampling nodes. Key words and phrases : trigonometric approximation, hyperbolic cross, sparse grid, fast Fourier transform, nonequispaced FFT 2010 AMS Mathematics Subj...
Michael Döhler, Stefan Kunis, Daniel Potts
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMNUM
Authors Michael Döhler, Stefan Kunis, Daniel Potts
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