RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Fundam. Prikl. Mat., 2014, Volume 19, Issue 5, Pages 143–166 (Mi fpm1609)  

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

Asymptotic properties of Chebyshev splines with fixed number of knots

Yu. V. Malykhin

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: V. M. Tikhomirov expressed Kolmogorov widths of the class $W^r:=W^r_\infty[-1,1]$ in the space $C:=C[-1,1]$ as a norm of special splines: $d_N(W^r,C)=\|x_{N-r,r}\|_C$, $N\ge r$; these splines were named Chebyshev splines. The function $x_{n,r}$ is a perfect spline of order $r$ with $n$ knots. We study the asymptotic behaviour of Chebyshev splines for $r\to\infty$ and fixed $n$. We calculate the asymptotics of knots and the $C$-norm of $x_{n,r}$ and prove that $x_{n,r}/x_{n,r}(1)=T_{n+r}+o(1)$. As a corollary, we obtain that $d_{n+r}(W^r,C)/d_r(W^r,C)\sim A_nr^{-n/2}$ as $r\to\infty$.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00332


Full text: PDF file (276 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2016, 218:5, 647–663

Bibliographic databases:

UDC: 517.518.8

Citation: Yu. V. Malykhin, “Asymptotic properties of Chebyshev splines with fixed number of knots”, Fundam. Prikl. Mat., 19:5 (2014), 143–166; J. Math. Sci., 218:5 (2016), 647–663

Citation in format AMSBIB
\Bibitem{Mal14}
\by Yu.~V.~Malykhin
\paper Asymptotic properties of Chebyshev splines with fixed number of knots
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 5
\pages 143--166
\mathnet{http://mi.mathnet.ru/fpm1609}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431896}
\elib{http://elibrary.ru/item.asp?id=27567806}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 218
\issue 5
\pages 647--663
\crossref{https://doi.org/10.1007/s10958-016-3048-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85028241556}


Linking options:
  • http://mi.mathnet.ru/eng/fpm1609
  • http://mi.mathnet.ru/eng/fpm/v19/i5/p143

    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. Vasil'eva, “Widths of weighted Sobolev classes with constraints $f(a)=\cdots= f^{(k-1)}(a)=f^{(k)}(b)=\cdots=f^{(r-1)}(b)=0$ and the spectra of nonlinear differential equations”, Russ. J. Math. Phys., 24:3 (2017), 376–398  crossref  mathscinet  zmath  isi  scopus
  • Фундаментальная и прикладная математика
    Number of views:
    This page:156
    Full text:37
    References:18

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019