Publications de l'Institut Mathématique, Nouvelle Série Vol. 95[109], pp. 29–47 (2014) 

OPTIMAL QUADRATURE FORMULA IN THE SENSE OF SARD IN $\mathbf{K_2(P_3)}$ SPACEAbdullo R. Hayotov, Gradimir V. Milovanovic, Kholmat M. ShadimetovInstitute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan Mathematical Institute of Serbian Academy of Sciences and Arts, Beograd, SerbiaAbstract: We construct an optimal quadrature formula in the sense of Sard in the Hilbert space $K_2(P_3)$. Using Sobolev's method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove an asymptotic optimality of such a formula in the Sobolev space $L_2^{(3)}(0,1)$. The obtained optimal quadrature formula is exact for the trigonometric functions $\sin x$, $\cos x$ and for constants. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula. Keywords: optimal quadrature formulas, error functional, extremal function, Hilbert space, optimal coefficients Classification (MSC2000): 65D32 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.
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