호남수학학술지 (Honam Mathematical Journal)

  • 제30권3호
  • /
  • Pages.581-587
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  • 2008
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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A STUDY OF AVERAGE ERROR BOUND OF TRAPEZOIDAL RULE

  • Yang, Mee-Hyea (Department of Mathematics, The University of Incheon) ;
  • Hong, Bum-Il (Department of Mathematics, Kyung Hee University)
  • 투고 : 2008.08.08
  • 발행 : 2008.09.25
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초록

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 $c_rH^{2r+3}$ through direct computation of constants $c_r$ for r ${\leq}$ 2 under the assumption that we have subintervals (for simplicity equal length h) partitioning [0, 1].

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참고문헌

  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.

피인용 문헌

  1. ON A STUDY OF ERROR BOUNDS OF TRAPEZOIDAL RULE vol.36, pp.2, 2014, https://doi.org/10.5831/HMJ.2014.36.2.291