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

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

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
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} 

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

 SHARE:

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