Low-rank approximation of analytic kernels

Marcus Webb

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arXiv · 2509.14017

Low-rank approximation of analytic kernels

Marcus Webb

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Abstract

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.

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Marcus Webb. 2025-09-17. Low-rank approximation of analytic kernels. https://arxiv.org/abs/2509.14017

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