Trigonometric interpolation on lattice grids

Abstract

In this paper we construct non-aliasing interpolation spaces and Lagrange functions for lattice grids. We argue that lattice grids are good for trigonometric interpolation and support this claim by numerical experiments. A greedy algorithm allows us to embed hyperbolic crosses in our interpolation spaces, and numerical experiments indicate that lattice grids are at least as good as sparse grids for trigonometric interpolation. A straightforward FFT-algorithm for functions sampled on lattice grids allows for fast computation and good approximation.