Weighted balanced truncation method for approximating kernel functions by exponentials
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916721452908544 |
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| author | Lin, Yuanshen Xu, Zhenli Zhang, Yusu Zhou, Qi |
| author_facet | Lin, Yuanshen Xu, Zhenli Zhang, Yusu Zhou, Qi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted balanced truncation method for approximating kernel functions by exponentials Lin, Yuanshen Xu, Zhenli Zhang, Yusu Zhou, Qi Computational Physics Numerical Analysis 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. |
| title | Weighted balanced truncation method for approximating kernel functions by exponentials |
| topic | Computational Physics Numerical Analysis |
| url | https://arxiv.org/abs/2503.03183 |