Geodesic
Approximation of the gradient of a~function on the basis of a~special
Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1136-1147.

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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: empty sphere condition, families of convex sets, piecewise linear approximation.
Mots-clés : Delaunay triangulation 
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V. A. Klyachin. Approximation of the gradient of a~function on the basis of a~special. Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1136-1147. http://geodesic.mathdoc.fr/item/IM2_2018_82_6_a2/

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