A randomized trapezoidal quadrature rule is proposed for continuous functions which enjoy less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for the randomized rule are established while an error bound for classical trapezoidal quadrature is obtained for comparison. The randomized trapezoidal quadrature rule is shown to improve the order of convergence by half.

中文翻译：

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随机梯形正交

提出了一种随机梯形求积规则，用于连续函数，其规律性低于通常要求的规律性。实际上，我们考虑了一些分数 Sobolev 空间中的函数。建立了随机规则的各种误差范围，同时获得了经典梯形正交的误差范围以进行比较。显示随机梯形求积规则可将收敛阶数提高一半。