Mathematics > Numerical Analysis
arXiv:2509.14017 (math)
[Submitted on 17 Sep 2025 (v1), last revised 17 Jun 2026 (this version, v4)]
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.
Submission history
From: Marcus Webb [view email]
[v1]
Wed, 17 Sep 2025 14:24:47 UTC (51 KB)
[v2]
Mon, 29 Sep 2025 10:58:32 UTC (51 KB)
[v3]
Wed, 15 Oct 2025 12:33:42 UTC (51 KB)
[v4]
Wed, 17 Jun 2026 06:02:24 UTC (50 KB)
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