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arXiv · 2607.26866

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

Christian Rieger·Holger Wendland
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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.

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Christian Rieger, Holger Wendland. 2026-07-29. Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension. https://arxiv.org/abs/2607.26866

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