Convergence analysis of approximation formulas for analytic functions via duality for potential energy minimization
Abstract
We investigate the approximation formulas that were proposed by Tanaka & Sugihara (2019), in weighted Hardy spaces, which are analytic function spaces with certain asymptotic decay. Under the criterion of minimum worst error of $n$point approximation formulas, we demonstrate that the formulas are nearly optimal. We also obtain the upper bounds of the approximation errors that coincide with the existing heuristic bounds in asymptotic order by duality theorem for the minimization problem of potential energy.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 DOI:
 10.48550/arXiv.1906.03133
 arXiv:
 arXiv:1906.03133
 Bibcode:
 2019arXiv190603133H
 Keywords:

 Mathematics  Numerical Analysis
 EPrint:
 17 pages