Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension
arXiv:2607.26866
summary
The paper develops new sampling inequalities for sparse grids combined with anchored projection to efficiently approximate high-dimensional Sobolev functions that exhibit effective low-dimensional behavior.
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.
Topics & keywords
#sparse grids#high-dimensional approximation#sampling inequalities#sobolev mixed regularity#anchored projection#low-dimensional structuresampling inequalitysparse gridSobolev mixed regularityanchored projectionregression processnon-matching sampling