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



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufimsk. Mat. Zh., 2009, Volume 1, Issue 4, Pages 110–118 (Mi ufa34)  

This article is cited in 1 scientific paper (total in 1 paper)

On trigonometric form of tchebyshev alternance theorems and on phase iterative method of finding best approximations with weight

V. I. Lebedev

Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: The article contains generalization of phase method of finding best approximations for function (in $C[-1,1]$) with weight by use of tchebyshev system of functions, rational functions and trigonometric polynomials. In the article P. L. Tchebyshev's alternance theorems have been attached analytical and constructive trigonometric form of weighted error $r(x)$ representation by means of phase function $\psi(\theta)$: $E\cos(m\theta+\psi(\theta))$, $x=\cos\theta$. Have been formulated iterative methods of finding approximation parameters. Mentioned numerical calculations examples reveal a high effciency of suggested solution method of those formulated extremal problems.

Keywords: T-systems, rational functions, trigonometric polynomials, formula of tchebyshev alternance, best approximations, phase iteration method.

Full text: PDF file (205 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 517.518.82
Received: 28.10.2009

Citation: V. I. Lebedev, “On trigonometric form of tchebyshev alternance theorems and on phase iterative method of finding best approximations with weight”, Ufimsk. Mat. Zh., 1:4 (2009), 110–118

Citation in format AMSBIB
\Bibitem{Leb09}
\by V.~I.~Lebedev
\paper On trigonometric form of tchebyshev alternance theorems and on phase iterative method of finding best approximations with weight
\jour Ufimsk. Mat. Zh.
\yr 2009
\vol 1
\issue 4
\pages 110--118
\mathnet{http://mi.mathnet.ru/ufa34}
\zmath{https://zbmath.org/?q=an:1240.41077}


Linking options:
  • http://mi.mathnet.ru/eng/ufa34
  • http://mi.mathnet.ru/eng/ufa/v1/i4/p110

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Уфимский математический журнал
    Number of views:
    This page:439
    Full text:162
    References:51
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020