Numerical Aspects of the Tensor Product Multilevel Method for High-dimensional, Kernel-based Reconstruction on Sparse Grids
Numerical Analysis
2025-02-07 v1 Numerical Analysis
Abstract
This paper investigates the approximation of functions with finite smoothness defined on domains with a Cartesian product structure. The recently proposed tensor product multilevel method (TPML) combines Smolyak's sparse grid method with a kernel-based residual correction technique. The contributions of this paper are twofold. First, we present two improvements on the TPML that reduce the computational cost of point evaluations compared to a naive implementation. Second, we provide numerical examples that demonstrate the effectiveness and innovation of the TPML.
Cite
@article{arxiv.2502.03881,
title = {Numerical Aspects of the Tensor Product Multilevel Method for High-dimensional, Kernel-based Reconstruction on Sparse Grids},
author = {Markus Büttner and Rüdiger Kempf and Holger Wendland},
journal= {arXiv preprint arXiv:2502.03881},
year = {2025}
}