6 papers · 1 filter
Samplet compression for conditionally positive definite kernels and universal Kriging
Sara Avesani, Rüdiger Kempf, Michael Multerer +1
We present a samplet-based framework for the efficient numerical solution of saddle-point systems arising from conditionally positive definite (CPD) kernel approximation in general…
Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension
Rüdiger Kempf
We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator fr…
Nodal Representations for Kernel-Based Multilevel Interpolation
Lorenz Gollwitzer, Rüdiger Kempf, Holger Wendland
We study the kernel-based multilevel method for approximating or learning a multivariate function from scattered data, motivated in part by recent applications in sparse grid metho…
Multiscale scattered data analysis in samplet coordinates
Sara Avesani, Rüdiger Kempf, Michael Multerer +1
We study multiscale scattered data interpolation schemes for globally supported radial basis functions with focus on the Matérn class. The multiscale approximation is constructed…
Numerical Aspects of the Tensor Product Multilevel Method for High-dimensional, Kernel-based Reconstruction on Sparse Grids
Markus Büttner, Rüdiger Kempf, Holger Wendland
This paper investigates the approximation of functions with finite smoothness defined on domains with a Cartesian product structure. The recently proposed tensor product multilevel…
On Quasi-Localized Dual Pairs in Reproducing Kernel Hilbert Spaces
Helmut Harbrecht, Rüdiger Kempf, Michael Multerer
In scattered data approximation, the span of a finite number of translates of a chosen radial basis function is used as approximation space and the basis of translates is used for…