On an optimal quadrature formula in Sobolev space $L_2^{(m)} (0,1)$

Details On an optimal quadrature formula in Sobolev space $L_2^{(m)} (0,1)$ On an optimal quadrature formula in Sobolev space $L_2^{(m)} (0,1)$

2008-12-11

arxiv.org/abs/0812.2081v1

Mathematics

Numerical Analysis

22 pages, submitted to the journal "Applied mathematics and computation"

Scientific paper

In this paper in the space $L_2^{(m)}(0,1)$ the problem of construction of optimal quadrature formulas is considered. Here the quadrature sum consists on values of integrand at nodes and values of first derivative of integrand at the end points of integration interval. The optimal coefficients are found and norm of the error functional is calculated for arbitrary fixed $N$ and for any $m\geq 2$. It is shown that when $m=2$ and $m=3$ the Euler-Maclaurin quadrature formula is optimal.

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