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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, Volume 16, Issue 4, Pages 425–435
DOI: https://doi.org/10.18500/1816-9791-2016-16-4-425-435 (Mi isu692) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Scientific Part
Mathematics

Bernstein polynomials for a standard module function on the symmetric interval

I. V. Tikhonova, V. B. Sherstyukovb, M. A. Petrosovac

a Moscow State University, Faculty of Computational Mathematics and Cybernetics, GSP-1, 1-52, Leninskiye Gory, 119991, Moscow, Russia
b National Research Nuclear University MEPhI, 31, Kashirskoe shosse, 115409, Moscow, Russia
c Moscow Pedagogical State University, 1, M. Pirogovskaya str., 199296, Moscow, Russia
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DOI: https://doi.org/10.18500/1816-9791-2016-16-4-425-435
Abstract: Bernstein polynomials are studied on a symmetric interval. Basic relations connected with Bernstein polynomials for a standard module function are received. By the Templ's formula we establish recurrence relations from which the Popoviciu's expansion is derived. Suitable formulas for the first and second derivatives are found. As a result an explicit algebraic form for Bernstein polynomials is obtained. We also notice some corollaries.
Key words: Bernstein polynomials, module function approximation.
Bibliographic databases:
Document Type: Article
UDC: 517.518.82
Language: Russian
Citation: I. V. Tikhonov, V. B. Sherstyukov, M. A. Petrosova, “Bernstein polynomials for a standard module function on the symmetric interval”, Izv. Saratov Univ. Math. Mech. Inform., 16:4 (2016), 425–435
Citation in format AMSBIB
\Bibitem{TikShePet16}
\by I.~V.~Tikhonov, V.~B.~Sherstyukov, M.~A.~Petrosova
\paper Bernstein polynomials for a standard module function on the symmetric interval
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2016
\vol 16
\issue 4
\pages 425--435
\mathnet{http://mi.mathnet.ru/isu692}
\crossref{https://doi.org/10.18500/1816-9791-2016-16-4-425-435}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3584327}
\elib{https://elibrary.ru/item.asp?id=27675056}
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    • This publication is cited in the following 4 articles:
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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