Communications in Analysis and Geometry

Volume 17 (2009)

Number 4

On one extremal property of a regular simplex

Pages: 685 – 699

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n4.a5

Authors

Vladislav Babenko (Department of Mathematical Analysis, Dnepropetrovsk National University, Ukraine)

Yuliya Babenko (Department of Mathematical Analysis, Dnepropetrovsk National University, Ukraine)

Nataliya Parfinovych (Department of Mathematical Analysis, Dnepropetrovsk National University, Ukraine)

Dmytro Skorokhodov (Department of Mathematical Analysis, Dnepropetrovsk National University, Ukraine)

Abstract

In this paper, we show that the $L_p$-error of asymmetric linearapproximation of the quadratic function $Q({\mathbfx})=\sum_{j=1}^{d}x_j^2$ on simplices in $\RR^d$ of fixed volumeis minimized on regular simplices.

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