Kh. M. Shadimetov, “Weight optimal cubature formulas in Sobolev's periodic space”, Sib. Zh. Vychisl. Mat., 2:2 (1999), 185

Sibirskii Zhurnal Vychislitel'noi Matematiki

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 1999, Volume 2, Number 2, Pages 185–196 (Mi sjvm334)

This article is cited in 7 scientific papers (total in 7 papers)

Weight optimal cubature formulas in Sobolev's periodic space

Kh. M. Shadimetov

Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan, Tashkent

Full-text PDF (480 kB) Citations (7)

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Abstract: In the present paper the weight lattice optimal cubature formulas in the periodic Sobolev's space

{\tilde{L}}_{2}^{(m)} (Ω)

$\widetilde L_2^{(m)}(\Omega)$ are constructed. Under writing out of the algorithm of the construction the extremal function is found, and by means of the function the norm of the error functional of the cubature formula is calculated. Minimizing the norms, periodic Winier–Hopf's systems are obtained. Then the uniqueness solution to the system has been proved.

Received: 26.06.1998
Revised: 01.10.1998

Bibliographic databases:

Document Type: Article

UDC: 517.54

Language: Russian

Citation: Kh. M. Shadimetov, “Weight optimal cubature formulas in Sobolev's periodic space”, Sib. Zh. Vychisl. Mat., 2:2 (1999), 185–196

Citation in format AMSBIB

\Bibitem{Sha99}

\by Kh.~M.~Shadimetov

\paper Weight optimal cubature formulas in Sobolev's periodic space

\jour Sib. Zh. Vychisl. Mat.

\yr 1999

\vol 2

\issue 2

\pages 185--196

\mathnet{http://mi.mathnet.ru/sjvm334}

\zmath{https://zbmath.org/?q=an:0936.46025}

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https://www.mathnet.ru/eng/sjvm334

https://www.mathnet.ru/eng/sjvm/v2/i2/p185

This publication is cited in the following 7 articles:

Kh. M. Shadimetov, N. Kh. Mamatova, “Sostavnye kubaturnye formuly na reshetke”, Izv. vuzov. Matem., 2023, no. 11, 59–74
A. R. Hayotov, U. N. Khayriev, “Optimal quadrature formulas in the space $\widetilde{W_2}^{(m,m-1)}$ of periodic functions”, Vestnik KRAUNTs. Fiz.-mat. nauki, 40:3 (2022), 211–226
Hayotov A.R., Jeon S., Shadimetov Kh.M., “Application of Optimal Quadrature Formulas For Reconstruction of Ct Images”, J. Comput. Appl. Math., 388 (2021), 113313
Hayotov A.R., Jeon S., Lee C.-O., Shadimetov Kh.M., “Optimal Quadrature Formulas For Non-Periodic Functions in Sobolev Space and Its Application to Ct Image Reconstruction”, Filomat, 35:12 (2021), 4177–4195
Hayotov A.R., Jeon S., Lee Ch.-O., “on An Optimal Quadrature Formula For Approximation of Fourier Integrals in the Space l-2((1))”, J. Comput. Appl. Math., 372 (2020), 112713
Boltaev N., Hayotov A., Milovanovic G., Shadimetov Kh., “Optimal Quadrature Formulas For Fourier Coefficients in W-2((M,M-1)) Space”, J. Appl. Anal. Comput., 7:4 (2017), 1233–1266
Boltaev N.D., Hayotov A.R., Shadimetov Kh.M., “Construction of Optimal Quadrature Formulas For Fourier Coefficients in Sobolev Space”, Numer. Algorithms, 74:2 (2017), 307–336

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Sibirskii Zhurnal Vychislitel'noi Matematiki

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