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

Titelangaben

Büttner, Markus ; Kempf, Rüdiger ; Wendland, Holger:
Numerical Aspects of the Tensor Product Multilevel Method for High-Dimensional, Kernel-Based Reconstruction on Sparse Grids.
In: Journal of Scientific Computing. Bd. 106 (2026) . - 8.
ISSN 1573-7691
DOI: https://doi.org/10.1007/s10915-025-03144-0

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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.