호남수학학술지 (Honam Mathematical Journal)

  • 제29권2호
  • /
  • Pages.245-257
  • /
  • 2007
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ERROR BOUNDS OF TRAPEZOIDAL RULE ON SUBINTERVALS USING DISTRIBUTION

  • 투고 : 2007.03.22
  • 심사 : 2007.04.24
  • 발행 : 2007.06.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We showed in [2] that if $r\leq2$, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to $h^{2r+3}$ 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 $r\geq3$, 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 $Ch^8$.

키워드

참고문헌

  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.