On an optimal quadrature formula in Sobolev space L₂^(m) (0,1)

2008/12/11 by Shadimetov, Kh. M., Hayotov, A. R., Nuraliev, F. A.
#65D32 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.0812.2081

Abstract

In this paper in the space L₂^(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≥ 2. It is shown that when m=2 and m=3 the Euler-Maclaurin quadrature formula is optimal.

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