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

Year: 2026

Type: article

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.

Source: Journal of Scientific Computing

Authors: Büttner, Markus, Kempf, Rüdiger, Wendland, Holger

Institution: University of Bayreuth

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

OpenAlex ID: W7133327102

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