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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 12, Pages 59–70
DOI: https://doi.org/10.26907/0021-3446-2023-12-59-70 (Mi ivm9926) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the problem of optimal interpolation of functions

Kh. M. Shadimetovab, N. H. Mamatovacb

a Tashkent State Transport University, 1 Odilkhodjaev str., Tashkent, 100167 Republic of Uzbekistan
b V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9 University str., Tashkent, 100174 Republic of Uzbekistan
c Bukhara State University, 11 Muhammad Ikbol str., Bukhara 200118 Republic of Uzbekistan
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DOI: https://doi.org/10.26907/0021-3446-2023-12-59-70
Abstract: In this work, the problem of constructing optimal interpolation formulas is discussed. Here, first, an exact upper bound for the error of the interpolation formula in the Sobolev space is calculated. The existence and uniqueness of the optimal interpolation formula, which gives the smallest error, are proved. An algorithm for finding the coefficients of the optimal interpolation formula is given. By implementing this algorithm, the optimal coefficients are found.
Keywords: Sobolev space, extremal function, composite lattice optimal cubature formulas, error functional.
Received: 29.03.2023
Revised: 29.03.2023
Accepted: 29.05.2023
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 12, Pages 53–63
DOI: https://doi.org/10.3103/S1066369X23120071
Document Type: Article
UDC: 519.644
Language: Russian
Citation: Kh. M. Shadimetov, N. H. Mamatova, “On the problem of optimal interpolation of functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 12, 59–70; Russian Math. (Iz. VUZ), 67:12 (2023), 53–63
Citation in format AMSBIB
\Bibitem{ShaMam23}
\by Kh.~M.~Shadimetov, N.~H.~Mamatova
\paper On the problem of optimal interpolation of functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 12
\pages 59--70
\mathnet{http://mi.mathnet.ru/ivm9926}
\crossref{https://doi.org/10.26907/0021-3446-2023-12-59-70}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 12
\pages 53--63
\crossref{https://doi.org/10.3103/S1066369X23120071}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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