Published

On minimizing the linear interpolation error of convex quadratic functions and the optimal simplex

Long Chen

East Journal on Approximations, 14(3), 271--284, 2008

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ABSTRACT:

This paper shows that the optimal simplex, in the sense of minimizing the 
linear interpolation error of the quadratic function $u(x) = x^2$ measured in $L^p$-norm, is 
the equilateral simplex. It also contains several explicit formulae on the best interpolation 
error when the volume of the simplex is one.