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Mat. Zametki, 1996, Volume 60, Issue 4, Pages 504–510 (Mi mz1858)  

This article is cited in 5 scientific papers (total in 5 papers)

Approximation error for linear polynomial interpolation on $n$-simplices

Yu. A. Kilizhekov


Abstract: Let $W_n^2M$ be the class of functions $f\colon\Delta_n\to\mathbb R$ (when ($\Delta_n$ is an $n$-simplex) with bounded second derivative (whose absolute value does not exceed $M>0$) along any direction at an arbitrary point of the simplex $\Delta_n$. Let $P_{1,n}(f;x)$ be the linear polynomial interpolating $f$ at the vertices of the simplex. We prove that there exists a function $g\in W_n^2M$ such that for any $f\in W_n^2M$ and any $x\in\Delta_n$ one has
$$ |f(x)-P_{1,n}(f;x)|\leqslant g(x). $$


DOI: https://doi.org/10.4213/mzm1858

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English version:
Mathematical Notes, 1996, 60:4, 378–382

Bibliographic databases:

UDC: 517.51
Received: 19.04.1993

Citation: Yu. A. Kilizhekov, “Approximation error for linear polynomial interpolation on $n$-simplices”, Mat. Zametki, 60:4 (1996), 504–510; Math. Notes, 60:4 (1996), 378–382

Citation in format AMSBIB
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\by Yu.~A.~Kilizhekov
\paper Approximation error for linear polynomial interpolation on $n$-simplices
\jour Mat. Zametki
\yr 1996
\vol 60
\issue 4
\pages 504--510
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\crossref{https://doi.org/10.4213/mzm1858}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619427}
\zmath{https://zbmath.org/?q=an:0899.41002}
\transl
\jour Math. Notes
\yr 1996
\vol 60
\issue 4
\pages 378--382
\crossref{https://doi.org/10.1007/BF02305420}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WN90400026}


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    This publication is cited in the following articles:
    1. Borodachov S. Sorokina T., “An Optimal Multivariate Spline Method of Recovery of Twice Differentiable Functions”, Bit, 51:3 (2011), 497–511  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. Borodachov S., Sorokina T., “Optimal Recovery of Twice Differentiable Functions Based on Symmetric Splines”, J. Approx. Theory, 164:10 (2012), 1443–1459  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Babenko V.F. Leskevich T.Yu., “Approximation of Some Classes of Functions of Many Variables by Harmonic Splines”, Ukr. Math. J., 64:8 (2013), 1151–1167  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Borodachov S., “Optimal Recovery of Three Times Differentiable Functions on a Convex Polytope Inscribed in a Sphere”, J. Approx. Theory, 234 (2018), 51–63  crossref  mathscinet  zmath  isi  scopus
    5. R. Sh. Khasyanov, “Ermitova interpolyatsiya na simplekse”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:3 (2018), 316–327  mathnet  crossref  elib
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