Interpolation lattices for hyperbolic cross trigonometric polynomials
Sparse grid discretisations allow for a severe decrease in the number of degrees of freedom for high dimensional problems. The corresponding hyperbolic cross fast Fourier transform exhibits numerical instabilities already for moderate problem sizes. Therefore, the authors propose the use of oversampled lattice rules known from multivariate numerical integration, which allows for the highly effcient and perfectly stable evaluation and reconstruction of trigonometric polynomials using only one ordinary fast Fourier transform (FFT). Given is numerical evidence that reasonable small lattices exist such that this new method outperforms the sparse grid based hyperbolic cross FFT for realistic problem sizes.
scientific article; zbMATH DE number 5996046
scientific article