Year: 2026
Type: article
Abstract: We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from scattered data. This smoothness information is then incorporated into our approximation algorithm to improve the accuracy. Specifically, we employ least squares approximation using trigonometric polynomials in combination with frequency boxes of optimized aspect ratios. These frequency boxes allow for the application of the Nonequispaced Fast Fourier Transform (NFFT), which significantly accelerates the computation of the method. Our approach enables the efficient optimization of dozens of parameters to achieve high approximation accuracy with minimal overhead. Numerical experiments demonstrate the practical effectiveness of the proposed method.
Authors: Felix Bartel, Pascal Schröter
Institution: Chemnitz University of Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7148393336