On a Posteriori Error Bounds of Trapezoidal Rule
Bum-Il Hong, Intae Ryoo, Gon Khang · 2019
In this paper, we discuss the average case setting and the probabilistic setting of composite Trapezoidal rule assuming that the class of integrand on an interval [0], [1] is equipped with a variant of the r-fold wiener measure based on the a finite number of function values for numerical integration. Moreover, we compute a posteriori bounds on the error of Trapezoidal rule from a probabilistic point of view. This a new a posteriori error bound is better than a bound that is commonly used in practice.