The Sinc approximation applied to double-exponentially decaying functions is referred to as the DE-Sinc approximation. Because of its high efficiency, this method has been used in various applications. In the Sinc approximation, its mesh size and truncation numbers should be optimally selected to achieve its best performance. However, the standard selection formula has only been ``near-optimally'' selected because the optimal formula of the mesh size cannot be expressed in terms of elementary functions of truncation numbers. In this study, we propose two improved selection formulas. The first one is based on the concept by an earlier research that resulted in a better selection formula for the double-exponential formula. The formula performs slightly better than the standard one, but is still not optimal. As a second selection formula, we introduce a new parameter to propose truly optimal selection formula. We provide explicit error bounds for both selection formulas. Numerical comparisons show that the first formula gives a better error bound than the standard formula, and the second formula gives a much better error bound than the standard and first formulas.

翻译：应用于双指数衰减函数的Sinc逼近称为DE-Sinc逼近。由于效率高，该方法已广泛应用于各类问题。在Sinc逼近中，需最优选取网格尺寸和截断数以实现最佳性能。然而，标准选取公式仅能做到"近最优"选取，因为网格尺寸的最优公式无法用截断数的初等函数表示。本研究提出两种改进的选取公式：第一种基于早期研究中的概念，该研究为双指数公式提出了更优的选取公式。该公式表现略优于标准公式，但仍非最优。作为第二种选取公式，我们引入新参数，提出了真正意义上的最优选取公式。我们为两种选取公式提供了明确的误差界。数值比较表明，第一种公式给出的误差界优于标准公式，第二种公式给出的误差界则远优于标准公式和第一种公式。