A study on the average case error of composite Newton-Cotes quadratures

  • Authors:

  • Sung Hee Choi;Jung Ho Park;Yoon-Young Park

  • Affiliations:

  • Faculty of Computer and Information Sciences, Sun Moon University, Asan, Chungnam 336-708, Korea;Faculty of Computer and Information Sciences, Sun Moon University, Asan, Chungnam 336-708, Korea;Faculty of Computer and Information Sciences, Sun Moon University, Asan, Chungnam 336-708, Korea

  • Venue:
  • The Korean Journal of Computational & Applied Mathematics
  • Year:
  • 2003

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Abstract

We study the integration problem in which one wants to compute the approximation to the definite integral in the average case setting. We choose the composite Newton-Cotes quadratures as our algorithm and the function values at equally spaced sample points on the given interval [0,1] as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal (modulo a multiplicative constant).