We show that if r≤2, the average error of the Trapezoidal rule is proportional to n^(-min{r+1, 3}) where n is the number of mesh points on the interval [0, 1]. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in t...
We show that if r≤2, the average error of the Trapezoidal rule is proportional to n^(-min{r+1, 3}) where n is the number of mesh points on the interval [0, 1]. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in the average case setting when r≤2.