4 papers
On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data
Michael Griebel, Guanglian Li, Christian Rieger
In many applications, random fields reflect uncertain parameters, and often their moments are part of the modeling process and thus well known. However, there are practical situati…
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…
Highly Localized RBF Lagrange Functions for Finite Difference Methods on Spheres
Wolfgang Erb, Thomas Hangelbroek, Francis J. Narcowich +2
The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the spheres can be used to create effective, stable finite difference methods based on radial basis…
On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data
Michael Griebel, Guanglian Li, Christian Rieger
Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--different…