Results 1 to 10 of about 538 (142)

Optimal quadrature formulas for oscillatory integrals in the Sobolev space

Journal of Inequalities and Applications, 2022
This work studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space L 2 ( m ) ( 0 , 1 ) $L_{2}^{(m)}(0,1)$ for numerical calculation of Fourier coefficients. Using Sobolev’s method, we obtain new sine and cosine
Kholmat Shadimetov, Abdullo Hayotov, Bakhromjon Bozarov   +2 more
doaj   +2 more sources

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, Abdullo Hayotov, Botir Abdikayimov   +2 more
doaj   +2 more sources

Weighted Optimal Quadrature Formulas in Sobolev Space and Their Applications

Algorithms
The optimization of computational algorithms is one of the main problems of computational mathematics. This optimization is well demonstrated by the example of the theory of quadrature and cubature formulas.
Kholmat Shadimetov, Khojiakbar Usmanov
doaj   +2 more sources

Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels

Axioms, 2022
The article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels.
Ilya Boykov, Vladimir Roudnev, Alla Boykova   +2 more
doaj   +1 more source

Optimal formulas for the approximate-analytical solution of the general Abel integral equation in the Sobolev space

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, Bakhtiyor S. Daliev   +1 more
doaj   +1 more source

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., Nuraliev, F.A., Parovik, R.I., Shadimetov, Kh.M.   +3 more
doaj   +1 more source

Optimization of the Approximate Integration Formula Using the Discrete Analogue of a High-Order Differential Operator

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, Aziz Boltaev, Roman Parovik   +2 more
doaj   +1 more source

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.
doaj   +1 more source

The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves

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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Optimal Numerical Integration

Кібернетика та комп'ютерні технології, 2020
Introduction. In many applied problems, such as statistical data processing, digital filtering, computed tomography, pattern recognition, and many others, there is a need for numerical integration, moreover, with a given (often quite high) accuracy ...
V.K. Zadiraka, L.V. Luts, I.V. Shvidchenko   +2 more
doaj   +1 more source