Low-rank approximation of analytic kernels
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912647656505344 |
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| author | Webb, Marcus |
| author_facet | Webb, Marcus |
| contents | Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This paper provides a framework for bounding the best low-rank approximation error of matrices arising from samples of a kernel that is analytically continuable in one of its variables to an open region of the complex plane. Elegantly, the low-rank approximations used in the proof are computable by rational interpolation using the roots and poles of Zolotarev rational functions, leading to a fast algorithm for their construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-rank approximation of analytic kernels Webb, Marcus Numerical Analysis Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This paper provides a framework for bounding the best low-rank approximation error of matrices arising from samples of a kernel that is analytically continuable in one of its variables to an open region of the complex plane. Elegantly, the low-rank approximations used in the proof are computable by rational interpolation using the roots and poles of Zolotarev rational functions, leading to a fast algorithm for their construction. |
| title | Low-rank approximation of analytic kernels |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.14017 |