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Optimal quadrature formulas in the space W2(m,m−1) of periodic functions
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022 This paper is devoted to the process of finding the upper bound for the absolute error of the optimal quadrature formula in the space W2(m,m−1) of real-valued, periodic functions. For this the extremal function of the quadrature formula is used.
Hayotov, A.R., Khayriev, U.N.
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On an Optimal Quadrature Formula in a Hilbert Space of Periodic Functions
Algorithms, 2022 The present work is devoted to the construction of optimal quadrature formulas for the approximate calculation of the integrals ∫02πeiωxφ(x)dx in the Sobolev space H˜2m.
Kholmat Shadimetov +2 more
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Mathematics, 2023 It is known that discrete analogs of differential operators play an important role in constructing optimal quadrature, cubature, and difference formulas.
Kholmat Shadimetov +2 more
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Results in Applied Mathematics, 2022 This article discusses the development of a new algorithm, which is based on optimal quadrature formulas for obtaining solutions to the generalized Abel integral equations.
Kholmat M. Shadimetov +1 more
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Some Generalized Error Inequalities and Applications
Journal of Inequalities and Applications, 2008 We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson's , and Lobatto four-point quadrature rule for twice-differentiable mapping. Moreover, it is shown that the corresponding optimal quadrature formula presents
Mir NazirAhmad, Zafar Fiza
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Euler-Maclaurin type optimal formulas for numerical integration in Sobolev space
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2020 In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space L2(m)(0,1) is considered. Here the quadrature sum consists of values of the integrand at nodes and values of the first and the third ...
Hayotov, A.R. +3 more
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Optimal quadrature formulas in Sobolev space for solving the generalized Abel integral equation [PDF]
E3S Web of ConferencesIn this article, a composite optimal quadrature formula is constructed for an approximate analytical solution of the generalized integral Abel equation in the Sobolev functional space.
Daliyev Bakhtiyor +5 more
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A New First Order Expansion Formula with a Reduced Remainder
Axioms, 2022 This paper is devoted to a new first order Taylor-like formula, where the corresponding remainder is strongly reduced in comparison with the usual one, which appears in the classical Taylor’s formula.
Joel Chaskalovic, Hessam Jamshidipour
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Моделирование и анализ информационных систем, 2013 In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm
K. Tukhliev
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Estimates of the error of interval quadrature formulas on some classes of differentiable functions
Researches in Mathematics, 2020 The exact value of error of interval quadrature formulas $$\int_0^{2\pi}f(t)dt -\frac{\pi}{nh}\sum_{k=0}^{n-1}\int_{-h}^hf(t+\frac {2k\pi}{n})dt = R_n(f;\vec{c_0};\vec{x_0};h)$$ obtained for the classes $W^rH^{\omega} (r=1,2,...)$ of differentiable ...
V.P. Motornyi, D.A. Ovsyannikov
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