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, the 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。由于该方法具有高效率，已被广泛应用于各类场景。在Sinc逼近中，为实现最佳性能，需对网格尺寸和截断数进行最优选取。然而，标准选取公式仅能达到"近最优"效果，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选取公式：第一种基于前人研究中针对双指数公式提出的更优选取概念，该公式性能略优于标准公式但尚未达到最优；第二种通过引入新参数提出真正的最优选取公式。我们为两种选取公式提供了显式误差界。数值对比表明：第一种公式的误差界优于标准公式，而第二种公式的误差界远优于标准公式和第一种公式。