Author

Rüdiger Kempf

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Preprint Sep 2026

Anisotropic Kernel-based Multilevel Interpolation of High-Dimensional Functions on Sparse Grids

Using a recent nodal representation of the low-dimensional multilevel operators, an explicit, computable representation of the high-dimensional interpolant is derived, and the full range of anisotropy weights that attain the optimal rate against the number of degrees of freedom are characterised.

Rüdiger Kempf · 0 citations

Preprint Aug 2026

Samplet compression for conditionally positive definite kernels and universal Kriging

A samplet-based framework for the efficient numerical solution of saddle-point systems arising from conditionally positive definite (CPD) kernel approximation in general and universal Kriging in particular, which achieves O(N log N) cost for the assembly and the storage of the saddle-point system.

Sara Avesani, Rüdiger Kempf, M. Multerer et al. · 0 citations

Jul 2026

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension

An explicit budget allocation condition is derived from a coupled error analysis that interprets the surrogate as a reconstruction from approximate data and yields a decomposition of the total error into reconstruction and learning contributions that can be analyzed independently.

Rüdiger Kempf · arXiv.org · 0 citations