Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Tikhonov I. V., Sherstyukov V. B., Petrosova M. A. Bernstein Polynomials for a Standard Module Function on the Symmetric Interval. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 4, pp. 425-435. DOI: 10.18500/1816-9791-2016-16-4-425-435, EDN: XHPYIH

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.11.2016
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.518.82
DOI: 
10.18500/1816-9791-2016-16-4-425-435
EDN: 
XHPYIH

Bernstein Polynomials for a Standard Module Function on the Symmetric Interval

Autors: 
Tikhonov Ivan Vladimirovich, Lomonosov Moscow State University
Sherstyukov Vladimir Borisovich, National Research Nuclear University MEPhI
Petrosova Margarita Arsenovna, Moscow Pedagogical State University
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
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Received: 
22.07.2016
Accepted: 
24.10.2016
Published: 
30.11.2016
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