JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A STUDY OF AVERAGE ERROR BOUND OF TRAPEZOIDAL RULE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 30, Issue 3,  2008, pp.581-587
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2008.30.3.581
 Title & Authors
A STUDY OF AVERAGE ERROR BOUND OF TRAPEZOIDAL RULE
Yang, Mee-Hyea; Hong, Bum-Il;
  PDF(new window)
 Abstract
In this paper, to have a better a posteriori error bound of the average case error between the true value of I(f) and the Trapezoidal rule on subintervals using zero mean-Gaussian, we prove that a new average error between the difference of the true value of I(f) from the composite Trapezoidal rule and that of the composite Trapezoidal rule from the simple Trapezoidal rule is bounded by through direct computation of constants for r 2 under the assumption that we have subintervals (for simplicity equal length h) partitioning [0, 1].
 Keywords
Trapezoidal rule;Error analysis;Wiener measure;
 Language
English
 Cited by
1.
ON A STUDY OF ERROR BOUNDS OF TRAPEZOIDAL RULE,;;

호남수학학술지, 2014. vol.36. 2, pp.291-303 crossref(new window)
1.
ON A STUDY OF ERROR BOUNDS OF TRAPEZOIDAL RULE, Honam Mathematical Journal, 2014, 36, 2, 291  crossref(new windwow)
 References
1.
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975.

2.
N. Hahm and B. I. Hong, An Error of composite Trapezoidal Rule, J. of Appl. Math. &. Computing 13 (2003), 365-372.

3.
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.

4.
H. H. Kuo, Gaussian Measure in Banach Spaces, Lecture Notes in Mathematics 463, Springer-Verlag, Berlin.

5.
E. Novak, Deterministic and Stochastic Error Bound in Numerical Analysis Lecture Notes in Mathematics 1349, Springer-Verlag, Berlin, 1988.

6.
A. V. Skorohod, Integration in Hilbert Space, Springer-Verlag, New York, 1974.

7.
J. F. Traub, G. W. Wasilkowski and H. Wozniakowski, Information-Based Complexity, Academic Press, New York, 1988.

8.
N. N. Vakhania, Probability distributed on Linear Spaces, North-Holland, New York, 1981.