Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_2^{m,m-1}(0,1)$ Space

Details Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_2^{m,m-1}(0,1)$ Space Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_2^{m,m-1}(0,1)$ Space

2008-10-30

arxiv.org/abs/0810.5421v1

Mathematics

Numerical Analysis

17 pages, this paper was published in Uzbek Mathematical Journal, 2004, \No3

Scientific paper

In this paper problem of construction of optimal quadrature formulas in
$W_2^{(m,m-1)}(0,1)$ space is considered. Here by using Sobolev's algorithm
when $m=1,2$ we find the optimal coefficients of the quadrature formulas of the
form $$ \int\limits_0^1\phi(x)dx\cong
\sum\limits_{\beta=0}^NC_{\beta}\phi(x_{\beta}). $$

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