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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, Volume 15, Issue 3, Pages 288–300
DOI: https://doi.org/10.18500/1816-9791-2015-15-3-288-300 (Mi isu595) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Mathematics

Gluing rule for Bernstein polynomials 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 st., 199296, Moscow, Russia
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DOI: https://doi.org/10.18500/1816-9791-2015-15-3-288-300
Abstract: We study special laws that arise in a sequence of the Bernstein polynomials on a symmetric interval. In particular, we set the exact rule of regular pairwise coincidence (gluing rule) which is acting for the Bernstein polynomials of a piecewise linear generating function with rational abscissas of break points. The accuracy of this rule for convex piecewise linear generating functions is shown. The possibility of “random” gluing for the Bernstein polynomials in a non-convex case is noted. We give also some examples and illustrations.
Key words: Bernstein polynomials, symmetric interval, piecewise linear functions, gluing rule.
Bibliographic databases:
Document Type: Article
UDC: 517.518.82
Language: Russian
Citation: I. V. Tikhonov, V. B. Sherstyukov, M. A. Petrosova, “Gluing rule for Bernstein polynomials on the symmetric interval”, Izv. Saratov Univ. Math. Mech. Inform., 15:3 (2015), 288–300
Citation in format AMSBIB
\Bibitem{TikShePet15}
\by I.~V.~Tikhonov, V.~B.~Sherstyukov, M.~A.~Petrosova
\paper Gluing rule for Bernstein polynomials on the symmetric interval
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 3
\pages 288--300
\mathnet{http://mi.mathnet.ru/isu595}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-3-288-300}
\elib{https://elibrary.ru/item.asp?id=24235222}
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    • This publication is cited in the following 6 articles:
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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