ON AN ERROR OF TRAPEZOIDAL RULE

  • Hong, Bum-Il (Department of Mathematics Kyung Hee University) ;
  • Choi, Sung-Hee (Division of Information and Computer Science Sun Moon University) ;
  • Hahm, Nahm-Woo (Institute of Natural Science Kyung Hee University)
  • Published : 1998.10.01

Abstract

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