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arXiv · 2502.03881

Numerical Aspects of the Tensor Product Multilevel Method for High-dimensional, Kernel-based Reconstruction on Sparse Grids

Markus Büttner·Rüdiger Kempf·Holger Wendland
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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.

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Markus Büttner, Rüdiger Kempf, Holger Wendland. 2025-02-06. Numerical Aspects of the Tensor Product Multilevel Method for High-dimensional, Kernel-based Reconstruction on Sparse Grids. https://arxiv.org/abs/2502.03881

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