New conformal map for the Sinc approximation for exponentially decaying functions over the semi-infinite interval
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The Sinc approximation has shown its high efficiency for numerical methods in many fields. Conformal maps play an important role in this regard; an appropriate conformal map should be employed to apply the Sinc approximation in general. Appropriate conformal maps were already proposed for typical cases, but it does not mean that they are optimal. In other words, if one employs another conformal map instead of existing one, the performance of the Sinc approximation may be improved. In this paper, we propose a new conformal map for the case where functions are defined over the semi-infinite interval and decay exponentially. Then, we show in both theoretical and numerical ways that the convergence rate is improved by replacing the existing conformal map with the proposed one.
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