We introduce the isoperimetry coefficient sigma(G) = vertical bar partial derivative G vertical bar(n/(n)-(1))/vertical bar G vertical bar of region G subset of R-n. In terms of this the error delta(Delta)(f) estimates for the gradient of the piecewise linear interpolation of functions of class C-1(G), C-2(G), C-1,C- (alpha) (G), 0 <alpha <1, are obtained. The problem of obtaining such estimates is nontrivial, especially in the multidimensional case. Here it should be noted that in the two-dimensional case, for functions of class C-2 (G), the convergence of the derivatives is provided by the classical Delaunay condition. In the multidimensional case, as shown by the examples, such conditions are not sufficient. Nevertheless, the article shows how to apply these estimates to the Delaunay triangulation of multidimensional discrete epsilon-nets. The results obtained give sufficient conditions for convergence of the derivatives on the Delaunay triangulation of discrete epsilon-nets with epsilon -> 0. In addition, the ratio of the distortion factor is found for isoperimetry coefficient under the quasi-isometric transformation.

Переведенное названиеIsoperimetry Coefficient for Simplex in the Problem of Approximation of Derivatives
Язык оригиналаРусский
Страницы (с-по)151-160
Число страниц10
ЖурналИзвестия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика
Номер выпуска2
СостояниеОпубликовано - 2015

Предметные области WoS

  • Математика