A. Hayotov

activity

20082021

most citedOptimal quadrature formulas for computing of Fourier integrals in a Hilbert space

55 citations · 105 across the 17 of their papers we have counts for

collaborators

17 papers

math.NA2021★ 55 cited

Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space

A. R. Hayotov, S. S. Babaev

In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\int_{a}^{b} e^{2 π iω x} φ (x) d x$ with $ω\in \mathbb{R…

math.NA2021★ 14 cited

On an optimal quadrature formula for approximation of Fourier integrals in the space $W_{2}^{(1, 0)}$

Samandar S. Babaev, A. R. Hayotov, U. N. Khayriev

The present paper is devoted to construction of an optimal quadrature formula for approximation of Fourier integrals in the Hilbert space $W_{2}^{(1, 0)} [a, b]$ of non-periodic, comple…

math.NA2020

Optimal quadrature formulas for non-periodic functions in Sobolev space and its application to CT image reconstruction

Abdullo R. Hayotov, Soomin Jeon, Chang-Ock Lee +1

In the present paper, optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\int_{a}^{b} e^{2 π iω x} φ (x) d x$ with $ω \in R$ i…

math.NA2019

The order of convergence of an optimal quadrature formula with derivative in the space $W_{2}^{(2, 1)}$

Abdullo R. Hayotov, Rashidjon G. Rasulov

The present work is devoted to extension of the trapezoidal rule in the space $W_{2}^{(2, 1)}$ . The optimal quadrature formula is obtained by minimizing the error of the formula by co…

math.NA2019★ 1 cited

Construction of optimal quadrature formulas exact for exponentional-trigonometric functions by Sobolev's method

A. K. Boltaev, A. R. Hayotov, Kh. M. Shadimetov

The paper studies Sard's problem on construction of optimal quadrature formulas in the space $W_{2}^{(m, 0)}$ by Sobolev's method. This problem consists of two parts: first calculatin…

math.NA2019★ 5 cited

On an optimal quadrature formula for approximation of Fourier integrals in the space $L_{2}^{(1)}$

Abdullo R. Hayotov, Soomin Jeon, Chang-Ock Lee

This paper deals with the construction of an optimal quadrature formula for the approximation of Fourier integrals in the Sobolev space $L_{2}^{(1)} [a, b]$ of non-periodic, complex va…

math.NA2014★ 1 cited

Optimal quadrature formulas with derivatives in Sobolev space

Kh. M. Shadimetov, A. R. Hayotov, F. A. Nuraliev

In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space $L_{2}^{(m)} (0, 1)$ is considered. Here the quadrature sum consists of…

math.NA2014★ 1 cited

Construction of interpolation splines minimizing the semi-norm in the space $K_{2} (P_{m})$

Abdullo R. Hayotov

In the present paper, using S.L. Sobolev's method, interpolation spline that minimizes the expression $\int_{0}^{1} (φ^{(m)} (x) + ω^{2} φ^{(m - 2)} (x))^{2} d x$ in the $K_{2} (P_{m})$ space are constru…

math.NA2013

The discrete analogue of the differential operator $\frac{d ^{2 m}}{d x ^{2 m}} + 2 ω^{2} \frac{d ^{2 m - 2}}{d x ^{2 m - 2}} + ω^{4} \frac{d ^{2 m - 4}}{d x ^{2 m - 4}}$

A. R. Hayotov

In the present paper we construct the discrete analogue $D_{m} (h β)$ of the differential operator $\frac{d^{2m}}{d x^{2m}} + 2ω^2\frac{d^{2m-2}}{d x^{2m-2}} + ω^4\frac{d^{2m-4}}{d x^{…

math.NA2012★ 4 cited

Construction of discrete analogue of the differential operator $\frac{d ^{4}}{d x ^{4}} + 2 \frac{d ^{2}}{d x ^{2}} + 1$ and its properties

A. R. Hayotov

In the present paper the discrete analogue of the differential operator $\frac{d ^{4}}{d x ^{4}} + 2 \frac{d ^{2}}{d x ^{2}} + 1$ is constructed and its some properties are proved.

math.NA2010

Optimal interpolation formulas in the periodic function space of S.L. Sobolev

Kh. M. Shadimetov, A. R. Hayotov, N. H. Mamatova

In this paper the problem of construction of lattice optimal interpolation formulas in the space $L_{2}^{(m)} (0, 1)$ is considered. Using S.L. Sobolev's method explicit f…

math.NA2010

Optimal Quadrature Formulas in the Sense of Sard in $W_{2}^{(m, m - 1)}$ Space

Kh. M. Shadimetov, A. R. Hayotov

In this paper in $W_{2}^{(m, m - 1)} (0, 1)$ space the problem of construction of optimal quadrature formula in the sense of Sard is considered and using S.L. Sobolev's method it is obtai…

math.NA2009★ 6 cited

Optimal Quadrature Formulas with Positive Coefficients in $L_{2}^{(m)} (0, 1)$ Space

Kh. M. Shadimetov, A. R. Hayotov

In the Sobolev space $L_{2}^{(m)} (0, 1)$ optimal quadrature formulas with the nodes (1.5) are investigated. For optimal coefficients explicit form are obtained and norm of the error f…

math.NA2008★ 5 cited

On an optimal quadrature formula in Sobolev space $L_{2}^{(m)} (0, 1)$

Kh. M. Shadimetov, A. R. Hayotov, F. A. Nuraliev

In this paper in the space $L_{2}^{(m)} (0, 1)$ the problem of construction of optimal quadrature formulas is considered. Here the quadrature sum consists on values of integrand at nod…

math.NA2008

Calculation of the Norm of the Error Functional of Optimal Quadrature Formulas in the Space $W_{2}^{(2, 1)} (0, 1)$

A. R. Hayotov

In this paper in the space $W_{2}^{(2, 1)} (0, 1)$ square of the norm of the error functional of a optimal quadrature formula is calculated.

math.NA2008★ 5 cited

Properties of Discrete Analogue of the Differential Operator $\frac{d ^{2 m}}{d x ^{2 m}} - \frac{d ^{2 m - 2}}{d x ^{2 m - 2}}$

Kh. M. Shadimetov, A. R. Hayotov

In the paper properties of the discrete analogue $D_{m} (h β)$ of the differential operator $\frac{d ^{2 m}}{d x ^{2 m}} - \frac{d ^{2 m - 2}}{d x ^{2 m - 2}}$ are studied. It is known, that zeros of…

math.NA2008★ 8 cited

Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_{2}^{m, m - 1} (0, 1)$ Space

Kh. M. Shadimetov, A. R. Hayotov

In this paper problem of construction of optimal quadrature formulas in $W_{2}^{(m, m - 1)} (0, 1)$ space is considered. Here by using Sobolev's algorithm when $m = 1, 2$ we find the optimal…

Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space

On an optimal quadrature formula for approximation of Fourier integrals in the space W2(1,0)​

Optimal quadrature formulas for non-periodic functions in Sobolev space and its application to CT image reconstruction

The order of convergence of an optimal quadrature formula with derivative in the space W2(2,1)​

Construction of optimal quadrature formulas exact for exponentional-trigonometric functions by Sobolev's method

On an optimal quadrature formula for approximation of Fourier integrals in the space L2(1)​

Optimal quadrature formulas with derivatives in Sobolev space

Construction of interpolation splines minimizing the semi-norm in the space K2​(Pm​)

The discrete analogue of the differential operator dx2md2m​+2ω2dx2m−2d2m−2​+ω4dx2m−4d2m−4​

Construction of discrete analogue of the differential operator dx4d4​+2dx2d2​+1 and its properties

Optimal interpolation formulas in the periodic function space of S.L. Sobolev

Optimal Quadrature Formulas in the Sense of Sard in W2(m,m−1)​ Space

Optimal Quadrature Formulas with Positive Coefficients in L2(m)​(0,1) Space

On an optimal quadrature formula in Sobolev space L2(m)​(0,1)

Calculation of the Norm of the Error Functional of Optimal Quadrature Formulas in the Space W2(2,1)​(0,1)

Properties of Discrete Analogue of the Differential Operator dx2md2m​−dx2m−2d2m−2​

Calculation of Coefficients of the Optimal Quadrature Formulas in the W2m,m−1​(0,1) Space

On an optimal quadrature formula for approximation of Fourier integrals in the space $W_{2}^{(1, 0)}$

The order of convergence of an optimal quadrature formula with derivative in the space $W_{2}^{(2, 1)}$

On an optimal quadrature formula for approximation of Fourier integrals in the space $L_{2}^{(1)}$

Construction of interpolation splines minimizing the semi-norm in the space $K_{2} (P_{m})$

The discrete analogue of the differential operator $\frac{d ^{2 m}}{d x ^{2 m}} + 2 ω^{2} \frac{d ^{2 m - 2}}{d x ^{2 m - 2}} + ω^{4} \frac{d ^{2 m - 4}}{d x ^{2 m - 4}}$

Construction of discrete analogue of the differential operator $\frac{d ^{4}}{d x ^{4}} + 2 \frac{d ^{2}}{d x ^{2}} + 1$ and its properties

Optimal Quadrature Formulas in the Sense of Sard in $W_{2}^{(m, m - 1)}$ Space

Optimal Quadrature Formulas with Positive Coefficients in $L_{2}^{(m)} (0, 1)$ Space

On an optimal quadrature formula in Sobolev space $L_{2}^{(m)} (0, 1)$

Calculation of the Norm of the Error Functional of Optimal Quadrature Formulas in the Space $W_{2}^{(2, 1)} (0, 1)$

Properties of Discrete Analogue of the Differential Operator $\frac{d ^{2 m}}{d x ^{2 m}} - \frac{d ^{2 m - 2}}{d x ^{2 m - 2}}$

Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_{2}^{m, m - 1} (0, 1)$ Space