On the optimal analytic continuation from discrete data

2021/06/02 by Narek Hovsepyan, Hovsepyan, Narek
Computer Science · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2106.01471

openalex publication_date 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider analytic functions from a reproducing kernel Hilbert space. Given that such a function is of order ε on a set of discrete data points, relative to its global size, we ask how large can it be at a fixed point outside of the data set. We obtain optimal bounds on this error of analytic continuation and describe its asymptotic behavior in ε. We also describe the maximizer function attaining the optimal error in terms of the resolvent of a positive semidefinite, self-adjoint and finite rank operator.

Citations

• On feasibility of extrapolation of the complex electromagnetic permittivity function using Kramer-Kronig relations

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