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

翻译：为连续功能建议了一个随机化的捕捉性捕捉性二次曲线规则,这些函数的规律性比通常要求的要低。 事实上,我们考虑的是某些小块的索博列夫空间的函数。 确定这种随机化规则的各种错误界限,同时获得一个用于比较传统捕捉性二次曲线的错误。 随机化的捕捉性二次曲线规则显示,随机化的捕捉性二次曲线规则可以将趋同的顺序提高一半。