Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension
Numerical Analysis
2026-07-29 v1
Abstract
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.
Cite
@article{arxiv.2607.26866,
title = {Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension},
author = {Christian Rieger and Holger Wendland},
journal= {arXiv preprint arXiv:2607.26866},
year = {2026}
}