Multidimensional Fourier Transform on Sparse Grids

Abstract

When working on multidimensional problems, the number of points needed when using a tensor product grid. This is known as the curse of dimensionality. In this thesis we propose a set of sparse grids, which can be used to dampen this curse. The grid is chosen such that we can apply the Fourier transform on functions sampeled on it. The thesis describes such an algorithm.