Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle

The main results of this paper are the analysis of the quality of approximation of polynomial interpolation and the computation of the approximate optimal interpolation points in the triangle. We introduce various norms for the interpolation operator. Computational results indicate that for a given polynomial degree, the set that minimizes the mean L(2) norm of the interpolation operator is close to the smallest Lebesgue constant interpolation set. In particular, for the triangle, this set gives the smallest Lebesgue constant currently known.