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http://dx.doi.org/10.3745/KIPSTA.2005.12A.5.391

An Error Bound of Trapezoidal Rule on Subintervals using Zero-mean Gaussian  

Hong, Bum-Il (경희대학교 전자정보대학)
Hahm, Nahm-Woo (인천대학교 수학과)
Yang, Mee-Hyea (인천대학교 수학과)
Abstract
In this paper, we study the average case error of the Trapezoidal rule using zero mean-Gaussian. Assume that we have n subintervals (for simplicity equal length) partitioning [0,1] and that each subinterval has the length h. Then, for $r{\leq}2$, we show that the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by $h^{2r+3}$ through direct computation of constants $c_r$.
Keywords
Average Case Error; Numerical Integration; Trapezoidal Rule;
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