On an exponential-trigonometric natural interpolation spline

Boltaev, A.K.; Akhmedov, Dilshod

doi:10.1063/5.0057116

Cited by 11 publications

(4 citation statements)

References 14 publications

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“…Indeed, from (14), it is clear that finding the smallest value of the norm of the error functional by coefficients at fixed nodes x β is equivalent to the best approximation of function…”

Section: Research On the Existence And Uniqueness Of An Optimal Quadr...mentioning

confidence: 99%

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Weighted Optimal Formulas for Approximate Integration

Shadimetov,

Jalolov

2024

Mathematics

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Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in the current work, we consider a discrete analogue of the differential operator 1−12π2d2dx2m in the Hilbert space H2μR, called Dmβ. We modify the Sobolev algorithm to construct optimal quadrature formulas using a discrete operator. We provide a weighted optimal quadrature formula, using this algorithm for the case where m=1. Finally, we construct an optimal quadrature formula in the Hilbert space H2μR for the weight functions px=1 and px=e2πiωx when m=1.

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“…Indeed, from (14), it is clear that finding the smallest value of the norm of the error functional by coefficients at fixed nodes x β is equivalent to the best approximation of function…”

Section: Research On the Existence And Uniqueness Of An Optimal Quadr...mentioning

confidence: 99%

“…These methods include the spline method [1][2][3], the φ-function method (as seen in [4][5][6][7][8][9]) and the Sobolev method [10][11][12][13]. Many authors have studied the Sard problem using these methods in different spaces (refer to [14][15][16][17][18][19][20][21][22] and the related literature).…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Weighted Optimal Formulas for Approximate Integration

Shadimetov,

Jalolov

2024

Mathematics

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“…Finally, taking into account the equalities ( 23)-( 24) and using the formula for the sum of an infinitely killing geometric progression, from (22) we obtain…”

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

confidence: 99%

“…-the optimal quadrature and interpolation formulas which are exact to the exponential-trigonometric functions were constructed [22], [23]; -In addition, a natural spline function that gives a minimum to the semi-norm in the corresponding space was found.…”

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

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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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