Dror Atariah, Günter Rote, and Mathijs Wintraecken:

Optimal triangulation of saddle surfaces

Abstract

We consider the piecewise linear approximation of saddle functions of the form f(x,y) = ax²-by² under the L_infinity error norm. We show that interpolating approximations are not optimal. One can get slightly smaller errors by allowing the vertices of the approximation to move away from the graph of the function.