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 Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 6, Pages 65–77 (Mi izv8691)

Approximation of the gradient of a function on the basis of a special class of triangulations

V. A. Klyachin

Abstract: We introduce the class of $\Phi$-triangulations of a finite set $P$ of points in $\mathbb{R}^n$ analogous to the classical Delaunay triangulation. Such triangulations can be constructed using the condition of empty intersection of $P$ with the interior of every convex set in a given family of bounded convex sets the boundary of which contains the vertices of a simplex of the triangulation. In this case the classical Delaunay triangulation corresponds to the family of all balls in $\mathbb{R}^n$. We show how $\Phi$-triangulations can be used to obtain error bounds for an approximation of the derivatives of $C^2$-smooth functions by piecewise linear functions.

Keywords: Delaunay triangulation, empty sphere condition, families of convex sets, piecewise linear approximation.

DOI: https://doi.org/10.4213/im8691

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English version:
Izvestiya: Mathematics, 2018, 82:6, 1136–1147

Bibliographic databases:

Document Type: Article
UDC: 514.174.3+519.65
MSC: 65D25, 65D07
Revised: 30.08.2017

Citation: V. A. Klyachin, “Approximation of the gradient of a function on the basis of a special class of triangulations”, Izv. RAN. Ser. Mat., 82:6 (2018), 65–77; Izv. Math., 82:6 (2018), 1136–1147

Citation in format AMSBIB
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