In computational contexts, analytic functions are often best represented by grid-based function values in the complex plane. For integrating periodic functions, the spectrally accurate trapezoidal rule (TR) then becomes a natural choice, due to both accuracy and simplicity. The two key present observations are (i) the accuracy of TR in the periodic case can be greatly increased (doubling or tripling the number of correct digits) by using function values also along grid lines adjacent to the line of integration and (ii) a recently developed end correction strategy for finite interval integrations applies just as well when using these enhanced TR schemes.

在计算环境中，解析函数通常最好由复杂平面中基于网格的函数值表示。对于积分周期函数，由于准确性和简便性，光谱精确的梯形规则（TR）成为自然选择。当前的两个主要观察结果是：（i）通过沿与积分线相邻的网格线使用函数值，可以大大提高周期性情况下TR的准确性（正确数字的数量增加或增加三倍），以及（ii）当使用这些增强的TR方案时，最近开发的用于有限间隔积分的末端校正策略同样适用。