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Ghizzetti A., Ossicini A. Quadrature Formulae, Akademie Verlag, Berlin (1970).

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Article

About Coefficients and Order of Convergence of the Optimal Quadrature Formula

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


American Journal of Numerical Analysis. 2014, Vol. 2 No. 2, 35-48
DOI: 10.12691/ajna-2-2-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Aziz K. Boltaev, Abdullo R. Hayotov, 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.

Correspondence to: Abdullo  R. Hayotov, Department of Computational Methods, Institute of Mathematics, National University of Uzbekistan, Do`rmon yo`li str. Tashkent, Uzbekistan. Email: hayotov@mail.ru

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, .

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