APPLICATION OF TRIGONOMETRIC WEIGHTING OPTIMAL QUADRATURE FORMULAS FOR RESTORATION OF COMPUTER TOMOGRAPHIC IMAGES

Optimal quadrature formulas with trigonometric weights

Authors

  • BAXROMJON BOZAROV TATUFF

Keywords:

cubature formulas, quadrature formulas, error function, norm of error function, optimal coefficients, Fourier integrals

Abstract

Optimal quadrature formulas with trigonometric weights can be applied to approximate trigonometric weighted integrals encountered in calculation of Fure coefficients, geomatematics, nuclear physics, signal processing, computed tomography, and many other practical issues.

References

Bozarov B.I. An optimal quadrature formula with weight function in the Sobolev space // Uzbek Mathematical Journal. – Tashkent, 2019, no 4, pp 47-53. 2. Bozarov B.I. Optimal quadrature formulas with the trigonometric weight in the Sobolev space // Bulletin of the Institute of Mathematics, V.I. Romanovskiy Institute of Mathematics. – Tashkent, 2020. no 4. pp.1-10.

Hayotov A.R., Bozarov B.I. An optimal quadrature formulas with the trigonometric weight in the Sobolev space // AIP Conference Proceeding, 2365, 020022 (2021), 16 July.

Bozarov B.I. An optimal quadrature formula in the Sobolev space // Uzbek Mathematical Journal. – Tashkent, 2021, no 3, pp 46-59. (01.00.00; №6).

Hayotov A.R., Bozarov B.I. Optimal quadrature formula with cosine weight function //Problems of Computational and Applied Mathematics. – Tashkent, 2021, no 4, -pp. 106-118.

Shadimetov Kh.M., Hayotov A.R., Bozarov B.I. Optimal quadrature formulas for oscillatory integrals in the Sobolev space. Journal of inequalities and applications. Springer. Article number: 103 (2022).

Boltaev N.D., Hayotov A.R., Milovanovic G.V., Shadimetov Kh.M., Optimal quadrature formulas for numerical evaluation of Fourier coefficients in Journal of Applied Analysis and Computation, 2017, Vol 7, Issue 4, 1233-1266.

Hayotov A.R., Soomin Jeon, Chang-Ock Lee, On an optimal quadrature formula for approximation of Fourier integrals in the space // Journal of Computational and Applied Mathematics. 372. July 2020. 112713.

Boltaev N.D., Hayotov A.R., Shadimetov Kh.M., Construction of optimal quadrature formulas for Fourier coefficients in Sobolev space, Numerical Algorithms, Springer, (2017), 74: 307-336, DOI 10.1007/s11075-016-150-7.

Babaev S.S., Hayotov A.R. Optimal interpolation formulas in the space // Calcolo, 2019. - 56:23.

Шадиметов Х.М. Оптимальные решетчатые квадратурные и кубатурные формулы в пространствах Соболева. – Ташкент: Фан ва технология, 2019.

Daliyev, B., Tukxtasinov, D., Bozarov, B., Sabirov, S., Abdullayev, J., & Ruzimatova, M. (2024, November). Optimal quadrature formulas in Sobolev space for solving the generalized Abel integral equation. In E3S Web of Conferences (Vol. 508, p. 04007). EDP Sciences.

Published

2024-06-05

How to Cite

BOZAROV, B. (2024). APPLICATION OF TRIGONOMETRIC WEIGHTING OPTIMAL QUADRATURE FORMULAS FOR RESTORATION OF COMPUTER TOMOGRAPHIC IMAGES: Optimal quadrature formulas with trigonometric weights. The Descendants of Al-Fargani, 1(2), 24–27. Retrieved from https://al-fargoniy.uz/index.php/journal/article/view/373

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