Weighted balanced truncation method for approximating kernel functions by exponentials

Yuanshen Lin; Zhenli Xu; Yusu Zhang; Qi Zhou

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arXiv · 2503.03183

Weighted balanced truncation method for approximating kernel functions by exponentials

Yuanshen Lin·Zhenli Xu·Yusu Zhang·Qi Zhou

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Abstract

Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted balanced truncation to construct an optimal model reduction method for compressing the number of exponentials in the sum-of-exponentials approximation of kernel functions. This method shows great promise in approximating long-range kernels, achieving over 4 digits of accuracy improvement for the Ewald-splitting and inverse power kernels in comparison with the classical balanced truncation. Numerical results demonstrate its excellent performance and attractive features for practical applications.

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BibTeX RIS

Yuanshen Lin, Zhenli Xu, Yusu Zhang, Qi Zhou. 2025-03-05. Weighted balanced truncation method for approximating kernel functions by exponentials. https://arxiv.org/abs/2503.03183

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