Construction of Optimal Interpolation Formulas in the Sobolev Space

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

doi:10.1007/s10958-022-06035-z

Cited by 17 publications

(2 citation statements)

References 11 publications

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“…This shows that we need the Fourier transform F [ Gm (x)]. Taking into account ( 8), (10), and also using the formulas ( 5) and ( 7), we have…”

Section: Equation (1) In the Class Of Harrow-shaped Functions Becomes...mentioning

confidence: 99%

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The discrete analogue of high-order differential operator and its application to finding coefficients of optimal quadrature formulas

Shadimetov,

Davronov

2023

Preprint

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The discrete analogue of the differential operator plays an important role in the construction of interpolation, quadrature and cubature formulas. In this work, we consider a discrete analogue $D_m(h\beta)$ of the differential operator $\frac{d^{2m}}{dx^{2m}}+1$ designed specifically for even natural numbers $m$. The effectiveness of this operator by constructing an optimal quadrature formula in the space $L_2^{(2,0)}(0,1)$ is shown. The errors of the optimal quadrature formula in $W_2^{(2,1)}(0,1)$ space and the optimal quadrature formula in $L_2^{(2,0)}(0,1)$ space are numerically compared. Numerical results showed that the error of the optimal quadrature formula what constructed in this work is smaller than the error of the quadrature formula constructed in $W_2^{(2,1)}(0,1)$ space. MSC: 41A05, 41A15, 65D30, 65D32, 65M60, 65L60.

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“…This shows that we need the Fourier transform F [ Gm (x)]. Taking into account ( 8), (10), and also using the formulas ( 5) and ( 7), we have…”

Section: Equation (1) In the Class Of Harrow-shaped Functions Becomes...mentioning

confidence: 99%

“…-Hermitian-type optimal quadrature and interpolation formulas were constructed in the work [9], [10];…”

Section: Introductionmentioning

confidence: 99%

The discrete analogue of high-order differential operator and its application to finding coefficients of optimal quadrature formulas

Shadimetov,

Davronov

2023

Preprint

Self Cite

View full text Add to dashboard Cite

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Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions

Shadimetov,

Gulomov

2023

J Math Sci

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Optimal quadrature formulas for the approximate calculation of the Riemann-Liouville fractional order integral

Shadimetov,

Nuraliev,

Toshboev

2024

Problems in the Textile and Light Industry in the Context of Integration of Science and Industry and Ways to Solve Them: Ptlici

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Construction of Optimal Interpolation Formulas in the Sobolev Space

Abstract: In the present paper, using the discrete analogue of the differential operator d 2m dx 2m , optimal interpolation formulas are constructed in the L (4) 2 (0, 1) space. The explicit formulas for coefficients of optimal interpolation formulas are obtained.

Cited by 17 publications

References 11 publications

The discrete analogue of high-order differential operator and its application to finding coefficients of optimal quadrature formulas

The discrete analogue of high-order differential operator and its application to finding coefficients of optimal quadrature formulas

Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions

Optimal quadrature formulas for the approximate calculation of the Riemann-Liouville fractional order integral

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