Error estimates with explicit constants for the Sinc approximation over infinite intervals
Provides rigorous error estimates for verified numerical computations, benefiting researchers in numerical analysis and scientific computing who need guaranteed accuracy.
The paper derives explicit, computable error bounds for the Sinc approximation over semi-infinite and infinite intervals, extending previous work that only covered finite intervals.
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.