Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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BOUNDS OF ZERO MEAN GAUSSIAN WITH COVARIANCE FOR AVERAGE ERROR OF TRAPEZOIDAL RULE

  • Hong, Bum-Il (Department of Mathematics and Institute of Natural Sciences, Kyung Hee University) ;
  • Choi, Sung-Hee (Division of Information and Computer Science, Sun Moon University) ;
  • Hahm, Nahm-Woo (Department of Mathematics, Inchon University)
  • Published : 2001.01.01

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Abstract

We showed in [2] that if r≤2, zero mean Gaussian of average error of the Trapezoidal rule is proportional to h/sub i//sup 2r+3/ on the interval [0,1]. In this paper, if r≥3, we show that zero mean Gaussian of average error of the Trapezoidal rule is bounded by Ch⁴/sub i/h⁴/sub j/.

Keywords

References

  1. Methods of Numerical Integration P.J.Davis;P.Rabinowitz
  2. Comm. Korean Math. Soc. v.13 On an Error of Trapezoidal Rule B.I.Hong;H.S.Choi;N.Hahm
  3. Lecture Notes in Mathematics v.463 Gaussian Measures in Banach Spaces H.H.Kuo
  4. Integration in Hilbert Space A.V.Skorohod
  5. Information-Based Complexity J.F.Traub;G.W.Wasilkowski;H.Wozniakowski
  6. Probability distributed on Linear Spaces N.N.Vakhania