About Coefficients and Order of Convergence of the Optimal Quadrature Formula

Aziz K. Boltaev¹, Abdullo R. Hayotov^1, and Kholmat M. Shadimetov¹

¹Department of Computational Methods, Institute of Mathematics, National University of Uzbekistan, Do`rmon yo`li str. Tashkent, Uzbekistan

Cite this paper:
Aziz K. Boltaev, Abdullo R. Hayotov and Kholmat M. Shadimetov. About Coefficients and Order of Convergence of the Optimal Quadrature Formula. American Journal of Numerical Analysis. 2014; 2(2):35-48. doi: 10.12691/ajna-2-2-2

Abstract

In this paper we construct an optimal quadrature formula in the sense of Sard in the Hilbert space K₂(P₃). Using S.L. Sobolev's method we obtain new optimal quadrature formula and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of convergence of the optimal formula. The obtained optimal quadrature formula is exact for the functions e^-x, .

Keywords:
optimal quadrature formulas error functional extremal function hilbert space optimal coefficients

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