3 papers
math.NA2026
Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension
Christian Rieger, Holger Wendland
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 projec…
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…
math.NA2017
-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs
Dinh Dũng, Michael Griebel, Vu Nhat Huy +1
In this article, we present a cost-benefit analysis of the approximation in tensor products of Hilbert spaces of Sobolev-analytic type. The Sobolev part is defined on a finite dime…