On one extremal property of a regular simplex
arXiv:1101.24961 citationsh-index: 11
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This is a theoretical result for approximation theory, establishing an extremal property of regular simplices.
The paper proves that for asymmetric linear approximation of the quadratic function on simplices with fixed volume, the L_p-error is minimized by regular simplices.
In this paper, we show that the $L_p$-error of asymmetric linear approximation of the quadratic function $Q({\mathbf x})=\sum_{j=1}^{d}x_j^2$ on simplices in $\RR^d$ of fixed volume is minimized on regular simplices.