Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension

The approximation of high-dimensional functions is a challenging task due to the often appearing curse of dimensionality.

In this paper, we combine sparse grid with anchored projection techniques to derive sampling inequalities for Sobolev functions of a dominating mixed regularity which are effectively low dimensional.

To this end, we derive new sampling inequalities for sparse grids and combine these with recently investigated regression processes of non-matching sampling processes.