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Matematicheskie Zametki, 1975, Volume 18, Issue 6, Pages 803–814 (Mi mzm7692)  

This article is cited in 4 scientific papers (total in 4 papers)

Interpolation by polyhedral functions

V. F. Babenkoa, A. A. Ligunb

a Dnepropetrovsk State University
b Dneprodzerzhinsk State Technical University
Full-text PDF (699 kB) Citations (4)
Abstract: A polyhedral function $l_{P(\Delta_n)}(f)$. interpolating a function $f$, defined on a polygon $\Phi$, is defined by a set of interpolating nodes $\Delta_n\subset\Phi$ and a partition $P(\Delta_n)$ of the polygon $\Phi$ into triangles with vertices at the points of $\Delta_n$. In this article we will compute for convex moduli of continuity the quatities
$$ E(H_\Phi^\omega;P(\Delta_n))=\sup_{f\in H_\Phi^\omega}\|f-l_{P(\Delta_n)}(f)\|, $$
and also give an asymptotic estimate of the quantities
$$ E_n(H_\Phi^\omega)=\inf_{\Delta_n}\inf_{P(\Delta_n)}E(H_\Phi^\omega;P(\Delta_n)). $$
Received: 04.11.1974
English version:
Mathematical Notes, 1975, Volume 18, Issue 6, Pages 1068–1074
DOI: https://doi.org/10.1007/BF01099983
Bibliographic databases:
UDC: 517.51
Language: Russian
Citation: V. F. Babenko, A. A. Ligun, “Interpolation by polyhedral functions”, Mat. Zametki, 18:6 (1975), 803–814; Math. Notes, 18:6 (1975), 1068–1074
Citation in format AMSBIB
\Bibitem{BabLig75}
\by V.~F.~Babenko, A.~A.~Ligun
\paper Interpolation by polyhedral functions
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 6
\pages 803--814
\mathnet{http://mi.mathnet.ru/mzm7692}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=397234}
\zmath{https://zbmath.org/?q=an:0318.41024}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 6
\pages 1068--1074
\crossref{https://doi.org/10.1007/BF01099983}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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