anchored projection 1high-dimensional approximation 1low-dimensional structure 1sampling inequalities 1sobolev mixed regularity 1sparse grids 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.NA2026
Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension
Christian Rieger, Holger Wendland
The paper develops new sampling inequalities for sparse grids combined with anchored projection to efficiently approximate high-dimensional Sobolev functions that exhibit effective…
math.NA2025
Vector-Valued Gaussian Processes for Approximating Divergence- or Rotation-free Vector Fields
Quoc Thong Le Gia, Ian Hugh Sloan, Holger Wendland
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, the…
math.NA2024
Constructive Approximation of High-Dimensional Functions with Small Efficient Dimension with Applications in Uncertainty Quantification
Christian Rieger, Holger Wendland
In this paper, we show that the approximation of high-dimensional functions, which are effectively low-dimensional, does not suffer from the curse of dimensionality. This is shown…