Year: 2025
Type: article
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. In this paper, we introduce a weighted balanced truncation method that significantly reduces the number of exponential terms required for an accurate representation of the kernel. This method shows great promise in approximating long-range kernels, achieving more than four digits of accuracy improvement for the Ewald splitting and inverse power kernels compared to classical balanced truncation. Numerical results demonstrate the attractive performance of the method and promising features for practical applications.
Source: Physical review. E
DOI: 10.1103/xsgv-zbvp
Authors: Yuanshen Lin, Zhenli Xu, Yusu Zhang, Qi Zhou
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2868650802, G5199764333, G6891451343
OpenAlex ID: W4411400681