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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2022, Volume 38, Number 1, Pages 131–146
DOI: https://doi.org/10.26117/2079-6641-2022-38-1-131-146
(Mi vkam530)
 

This article is cited in 4 scientific papers (total in 4 papers)

INFORMATION AND COMPUTATION TECHNOLOGIES

Construction of optimal interpolation formula exact for trigonometric functions by Sobolev's method

Kh. M. Shadimetovab, A. K. Boltaevcb, R. I. Parovikdc

a Tashkent State Transport University
b V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
c National University of Uzbekistan named after M. Ulugbek, Tashkent
d Vitus Bering Kamchatka State University
References:
Abstract: The paper is devoted to derivation of the optimal interpolation formula in $W_2^{(0,2)}(0,1)$ Hilbert space by Sobolev's method. Here the interpolation formula consists of a linear combination $\sum\limits_{\beta=0}^N C_\beta \phi (x_\beta)$ of the given values of a function $\phi$ from the space $W_2^{(0,2)}(0,1)$. The difference between functions and the interpolation formula is considered as a linear functional called the error functional. The error of the interpolation formula is estimated by the norm of the error functional. We obtain the optimal interpolation formula by minimizing the norm of the error functional by coefficients $C_\beta (z)$ of the interpolation formula. The obtained optimal interpolation formula is exact for trigonometric functions $\sin (x)$ and $\cos (x)$. At the end of the paper we give some numerical results which confirm the numerical convergence of the optimal interpolation formula.
Keywords: extremal function, error functional, Hilbert space, optimal interpolation formula, optimal coefficients, Sobolev's method.
Document Type: Article
UDC: 519.652
MSC: Primary 65D30; Secondary 65D32
Language: English
Citation: Kh. M. Shadimetov, A. K. Boltaev, R. I. Parovik, “Construction of optimal interpolation formula exact for trigonometric functions by Sobolev's method”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 38:1 (2022), 131–146
Citation in format AMSBIB
\Bibitem{ShaBolPar22}
\by Kh.~M.~Shadimetov, A.~K.~Boltaev, R.~I.~Parovik
\paper Construction of optimal interpolation formula exact for trigonometric functions by Sobolev's method
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2022
\vol 38
\issue 1
\pages 131--146
\mathnet{http://mi.mathnet.ru/vkam530}
\crossref{https://doi.org/10.26117/2079-6641-2022-38-1-131-146}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
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