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abstract:
Functions with bounded mixed derivatives allow for an effective approximation by trigonometric polynomials with Fourier coefficients supported on the hyperbolic cross.
Interpolating on sparse grid nodes, such an approximation can be computed by means of the hyperbolic cross fast Fourier transform (HCFFT) efficiently.
In this talk, we discuss a generalisation of the HCFFT to arbitrary sampling nodes. Moreover, we show that the interpolation on the sparse grid is mildly ill conditioned and give examples of stable spatial discretisations. |
