Error estimates with explicit constants for the Sinc approximation over infinite intervals

TL;DR

This paper derives explicit, computable error bounds for the Sinc approximation over infinite and semi-infinite intervals, enhancing the reliability of numerical methods for functions defined on unbounded domains.

Contribution

The paper extends explicit error estimates for the Sinc approximation to infinite and semi-infinite intervals, improving verified numerical computations.

Findings

Explicit error bounds are derived for infinite intervals.

The bounds improve the reliability of Sinc approximation in unbounded domains.

The results facilitate verified numerical computations for functions on infinite intervals.

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.