Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Izv. Saratov Univ. Math. Mech. Inform.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 3 scientific papers (total in 3 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
Full-text PDF (214 kB) Citations (3)
References:
PDF
HTML
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}
Linking options:
  • https://www.mathnet.ru/eng/isu692
  • https://www.mathnet.ru/eng/isu/v16/i4/p425
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
    Statistics & downloads:
    Abstract page:429
    Full-text PDF :151
    References:41
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024