Weight-adapted ANOVA kernels for high-dimensional periodic approximation
Abstract
In this paper, we construct normalized periodic kernels from univariate functions satisfying suitable moment conditions and derive sufficient conditions for high-order convolution approximation. Two computable quasi-interpolation schemes are obtained by discretizing the convolution integral using either a full tensor grid or random samples. In each case, the analysis separates the continuous convolution error from the error introduced by discretization. The contribution of kernel energy to the error exposes the dimensional dependence of tensor-product kernels and motivates our weight-adapted ANOVA constructions. Under suitable summability conditions on the weights, we establish convolution error and kernel energy estimates that yield dimension-uniform error bounds for the resulting quasi-interpolants. Numerical experiments corroborate the theoretical convergence rates and illustrate the effect of coordinate weighting on dimensional dependence.
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BibTeX
@misc{sun2026weightadapted,
title = {{Weight-adapted ANOVA kernels for high-dimensional periodic approximation}},
author = {Zhengjie Sun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19409},
eprint = {2610.19409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19409},
}
RIS
TY - UNPB
TI - Weight-adapted ANOVA kernels for high-dimensional periodic approximation
AU - Zhengjie Sun
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19409
UR - https://arxiv.org/abs/2610.19409
AB - In this paper, we construct normalized periodic kernels from univariate functions satisfying suitable moment conditions and derive sufficient conditions for high-order convolution approximation. Two computable quasi-interpolation schemes are obtained by discretizing the convolution integral using either a full tensor grid or random samples. In each case, the analysis separates the continuous convolution error from the error introduced by discretization. The contribution of kernel energy to the error exposes the dimensional dependence of tensor-product kernels and motivates our weight-adapted ANOVA constructions. Under suitable summability conditions on the weights, we establish convolution error and kernel energy estimates that yield dimension-uniform error bounds for the resulting quasi-interpolants. Numerical experiments corroborate the theoretical convergence rates and illustrate the effect of coordinate weighting on dimensional dependence.
ER -