Abstract
AbstractWe investigate the approximation formulas that were proposed by Tanaka & Sugihara (IMA J. Numer. Anal. 39(4):1957–1984, 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 a duality theorem for the minimization problem of potential energy.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Engineering