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
Mots-clés : Delaunay triangulation
@article{IM2_2018_82_6_a2,
author = {V. A. Klyachin},
title = {Approximation of the gradient of a~function on the basis of a~special},
journal = {Izvestiya. Mathematics },
pages = {1136--1147},
publisher = {mathdoc},
volume = {82},
number = {6},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_6_a2/}
}
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/