RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 1997, Volume 62, Issue 3, Pages 404–417 (Mi mz1622)  

This article is cited in 6 scientific papers (total in 6 papers)

On a method for interpolating functions on chaotic nets

O. V. Matveev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Suppose $m,n\in\mathbb N$, $m\equiv n(\operatorname{mod}2)$, $K(x)=|x|^m$ for $m$ odd, $K(x)=|x|^m\ln|x|$ for $m$ even ($x\in\mathbb R^n$), $\mathscr P$ is the set of real polynomials in $n$ variables of total degree $\le m/2$, and $x_1,…,x_N\in \mathbb R^n$. We construct a function of the form
$$ \sum_{j=1}^N\lambda_jK(x-x_j)+P(x), \qquadwhere\quad \lambda_j\in\mathbb R,\quad P\in\mathscr P,\quad \sum_{j=1}^N\lambda_jQ(x_j)=0\quad\forall Q\in\mathscr P, $$
coinciding with a given function $f(x)$ at the points $x_1,…,x_N$. Error estimates for the approximation of functions $f\in W_p^k(\Omega)$ and their $l$th-order derivatives in the norms $L_q(\Omega_\varepsilon)$ are obtained for this interpolation method, where $\Omega$ is a bounded domain in $\mathbb R^n$, $\varepsilon>0$, $\Omega_\varepsilon=\{x\in\Omega:\operatorname{dist}(x,\partial\Omega)>\varepsilon\}$.

DOI: https://doi.org/10.4213/mzm1622

Full text: PDF file (263 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 1997, 62:3, 339–349

Bibliographic databases:

UDC: 517.518
Received: 28.04.1994
Revised: 28.02.1996

Citation: O. V. Matveev, “On a method for interpolating functions on chaotic nets”, Mat. Zametki, 62:3 (1997), 404–417; Math. Notes, 62:3 (1997), 339–349

Citation in format AMSBIB
\Bibitem{Mat97}
\by O.~V.~Matveev
\paper On a method for interpolating functions on chaotic nets
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 3
\pages 404--417
\mathnet{http://mi.mathnet.ru/mz1622}
\crossref{https://doi.org/10.4213/mzm1622}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1620074}
\zmath{https://zbmath.org/?q=an:0920.41001}
\elib{http://elibrary.ru/item.asp?id=13254863}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 3
\pages 339--349
\crossref{https://doi.org/10.1007/BF02360875}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000072500900009}


Linking options:
  • http://mi.mathnet.ru/eng/mz1622
  • https://doi.org/10.4213/mzm1622
  • http://mi.mathnet.ru/eng/mz/v62/i3/p404

    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. Bejancu, A, “Local accuracy for radial basis function interpolation on finite uniform grids”, Journal of Approximation Theory, 99:2 (1999), 242  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Bejancu, A, “On the accuracy of surface spline approximation and interpolation to bump functions”, Proceedings of the Edinburgh Mathematical Society, 44 (2001), 225  crossref  mathscinet  zmath  isi
    3. Johnson, MJ, “The L-p-approximation order of surface spline interpolation for 1 <= p <= 2”, Constructive Approximation, 20:2 (2004), 303  crossref  mathscinet  zmath  isi  scopus
    4. Hangelbroek, T, “Error estimates for thin plate spline approximation in the disk”, Constructive Approximation, 28:1 (2008), 27  crossref  mathscinet  zmath  isi  elib  scopus
    5. Rieger Ch., Zwicknagl B., “Improved Exponential Convergence Rates By Oversampling Near the Boundary”, Constr. Approx., 39:2 (2014), 323–341  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Schaback R., “Superconvergence of Kernel-Based Interpolation”, J. Approx. Theory, 235 (2018), 1–19  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:272
    Full text:110
    References:42
    First page:1

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