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This article is cited in 5 scientific papers (total in 5 papers)
INFORMATION AND COMPUTATION TECHNOLOGIES
Optimal quadrature formulas in the space $\widetilde{W_2}^{(m,m-1)}$of periodic functions
A. R. Hayotova, U. N. Khayrievb a National University of Uzbekistan named after Mirzo Ulugbek
b V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
Abstract:
This paper is devoted to the process of finding the upper bound for the absolute error of the optimal quadrature formula in the space $\widetilde{W_2}^{(m,m-1)}$of real-valued, periodic functions. For this the extremal function of the quadrature formula is used. In addition, it is shown that the norm of the error functional for the optimal quadrature formula constructed in the space $\widetilde{W_2}^{(m,m-1)}$ is less than the value of the norm of the error functional for the optimal quadrature formula in the Sobolev space $\widetilde{L_2}^{(m)}$.
Keywords:
optimal quadrature formula, optimal coefficients, error of quadrature formula, the Hilbert space, the error functional, Fourier transform.
Citation:
A. R. Hayotov, U. N. Khayriev, “Optimal quadrature formulas in the space $\widetilde{W_2}^{(m,m-1)}$of periodic functions”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 40:3 (2022), 211–226
Linking options:
https://www.mathnet.ru/eng/vkam565 https://www.mathnet.ru/eng/vkam/v40/i3/p211
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Abstract page: | 56 | Full-text PDF : | 50 | References: | 19 |
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