Quadrature error
= Quadrature error
The difference between a weighted integral and a discrete approximation is a quadrature error. For a <Hölder continuous function> on a <partition of an interval> with mesh $\Delta$, a left endpoint approximation has error of order $\Delta^\alpha$. For a normalized window <indicator function>, only the two endpoint cells contribute and the error is bounded by a constant times $\Delta/h$.