ERROR BOUNDS OF TRAPEZOIDAL RULE ON SUBINTERVALS USING DISTRIBUTION

• Journal title : Honam Mathematical Journal
• Volume 29, Issue 2,  2007, pp.245-257
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2007.29.2.245
Title & Authors
ERROR BOUNDS OF TRAPEZOIDAL RULE ON SUBINTERVALS USING DISTRIBUTION
Hong, Bum-Il; Hahm, Nahm-Woo;

Abstract
We showed in [2] that if $\small{r\leq2}$, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to $\small{h^{2r+3}}$ using zero mean Gaussian distribution under the assumption that we have subintervals (for simplicity equal length) partitioning and that each subinterval has the length. In this paper, if $\small{r\geq3}$, we show that zero mean Gaussian distribution of average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by $\small{Ch^8}$.
Keywords
Trapezoidal rule;Error analysis;Wiener measure;
Language
English
Cited by
References
1.
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975.

2.
B. I. Hong, N. Hahm and M. Yang, An Error bounds of Trapezoidal Rule on subintervals using zero-mean Gaussian, J. of Korea information processing Soc. 12-A (2005), 391-394.

3.
H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Mathematics 463, Springer-Verlag, Berlin.

4.
E. Novak, Deterministic and Stochastic Error Bound in Numerical Analysis, Lecture Notes in Mathematics 1349, Springer-Verlag, Berlin, 1988.

5.
A. V. Skorohod, Integration in Hilbert Space, Springer-Verlag, New York, 1974.

6.
J. F. Traub, G. W. Wasilkowski and H. Wozniakowski, Information-Based Complexity, Academic Press, New York, 1988.

7.
N. N. Vakhania, Probability distributed on Linear Spaces, North-Holland, New York, 1981.