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http://dx.doi.org/10.3745/KIPSTA.2004.11A.5.401

On the Average Case Errors of Numerical Integration Rules using Interpolation  

Choi, Sung-Hee (선문대학교 컴퓨터정보학부)
Hwang, Suk-Hyung (선문대학교 컴퓨터정보학부)
Lee, Jeong-Bae (선문대학교 컴퓨터정보학부)
Hong, Bum-Il (경희대학교 수학과)
Publication Information
The KIPS Transactions:PartA / v.11A, no.5, 2004 , pp. 401-406 More about this Journal
Abstract
Among many algorithms for the integration problems in which one wants to compute the approximation to the definite integral in the average case setting, we study the average case errors of numerical integration rules using interpolation. In particular, we choose the composite Newton-Cotes quadratures and the function values at equally spaced sample points on the given interval as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal(modulo a multiplicative constant).
Keywords
Complexity Theory; Information-based Complexity; Partial Information; Average Case Error; Numerical Quadratures; Newton-Cotes Newton-Cotes Quadratures;
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