论文标题
随机梯形正交
A randomised trapezoidal quadrature
论文作者
论文摘要
提出了一个随机梯形正交规则，用于连续功能，其规律性比通常所要求的少。确实，我们考虑在某些部分Sobolev空间中的功能。建立了此随机规则的各种误差界限，而获得经典梯形正交限制的误差进行比较。显示随机梯形正交规则可将收敛顺序提高一半。
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.
