This article is cited in 2 papers

Minimal projections and largest simplices

M. V. Nevskij

Yaroslavl State University

Abstract: It is proved that the minimal norm $\theta_n$ of a projection in linear interpolation on the $n$-dimensional cube $Q_n=[0,1]^n$ satisfies the condition $\theta_n=O(n^{1/2})$, $n\in\mathrm{N}$. With the previous results of the author it means that $\theta_n\approx n^{1/2}$. The upper estimates are provided by the projection with knots of interpolation in vertices of а largest simplex in $Q_n$.

UDC: 517.51+514.17

Received: 22.11.2006