1 citations · 1 across the 4 of their papers we have counts for
4 papers
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…
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…
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…
Kernel-based Discretisation for Solving Matrix-Valued PDEs
Peter Giesl, Holger Wendland
In this paper, we discuss the solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for…