Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

AN ERROR OF THE COMPOSITE TRAPEZOIDAL RULE

  • Nahmwoo Hahm (Department of Mathematics, University of Incheon) ;
  • Hong, Bum-Il (Department of Mathematics and Institute of Natural Sciences, Kyung Hee University)
  • Published : 2003.09.01

⟨ Previous Next ⟩

Abstract

We show that if ${\gamma}$ $\leq$ 2, the average error of the composite Trapezoidal rule on two consecutive intervals is proportional to h$\^$2h+3/ where h is the length of each subinterval of 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 ${\gamma}$ $\leq$ 2.

Keywords

References

  1. Methods of Numerical Integration P.J.Davis;P.Rabinowitz
  2. Lecture Notes in Mathematics 463 Gaussian Measures in Banach Spaces H.H.Kuo
  3. Integration in Hilbert Space A.V.Skorohod
  4. Information-Based Complexity J.F.Traub;G.W.Wasilkowski;H.Wo$\'{z}$niakowski
  5. Probability distributed on Linear Spaces N.N.Vakhania