5 papers
Improved Convergence of Multilevel Moving Least-Squares Approximation
Robert Durst, Holger Wendland
Moving least-squares approximation is a popular method for approximating multivariate functions from given discrete data. For higher accuracy higher degree polynomials have to be u…
Kernel-based learning of manifold-to-manifold maps from scattered data
Daniel Fischer, Holger Wendland
We describe and analyze new methods for approximating manifold-to-manifold maps using only scattered data information. To this end, we first study kernel-based approximation method…
On multiscale quasi-interpolation of scattered scalar- and manifold-valued functions
Nir Sharon, Rafael Sherbu Cohen, Holger Wendland
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where m…
A kernel-based discretisation method for first order partial differential equations of evolution type
Tobias Ramming, Holger Wendland
We derive a new discretisation method for first order PDEs of arbitrary spatial dimension, which is based upon a meshfree spatial approximation. This spatial approximation is simil…
Zooming from Global to Local: A Multiscale RBF Approach
Quoc Thong Le Gia, Ian H Sloan, Holger Wendland
Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximati…