Error estimates with explicit constants for the Sinc approximation over infinite intervals
Numerical Analysis
2022-03-04 v3 Numerical Analysis
Abstract
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined with a proper variable transformation. The convergence rate has been analyzed for typical cases including finite, semi-infinite, and infinite intervals. Recently, for verified numerical computations, a more explicit, "computable" error bound has been given in the case of a finite interval. In this paper, such explicit error bounds are derived for other cases.
Cite
@article{arxiv.1610.06685,
title = {Error estimates with explicit constants for the Sinc approximation over infinite intervals},
author = {Tomoaki Okayama},
journal= {arXiv preprint arXiv:1610.06685},
year = {2022}
}
Comments
Keywords: Sinc approximation, conformal map, double-exponential transformation, infinite interval, error bound