The Sinc approximation applied to double-exponentially decaying functions is referred to as the DE-Sinc approximation. This approximation has notably been utilized for many applications because of its high efficiency. The Sinc approximation's mesh size and truncation numbers should be optimally selected to avail its full performance. However, the usual formula has only been ``near-optimally'' selected because the optimal formula between the two cannot be expressed in terms of elementary functions. In this study, we propose two improved formulas. The first one is based on the concept by an earlier research that produced an improved selection formula for the double-exponential formula. The formula performed better than the usual one, but was still not optimal. As a second formula, we introduce a new parameter to propose a truly optimal formula between the two. We give explicit error bounds for both formulas. Numerical comparisons show that the first formula gives a better error bound than the standard formula, and the second formula gives a far better error bound than both 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。该逼近因其高效性而被广泛用于众多应用领域。为充分发挥其性能，需优化选择Sinc逼近的网格尺寸与截断数。然而，由于二者之间的最优关系无法用初等函数表示，常用公式仅为"近似最优"选择。本研究提出两种改进公式：第一种基于前期研究中双指数公式选择公式的改进思路，其性能优于常规公式但尚未达到最优；第二种通过引入新参数，提出了真正意义上的最优选择公式。我们给出了这两种公式的显式误差界。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与第一种公式。