Polynomial Interpolation and Approximation of Real Functions 2: Symmetrical Interpolation for the Triangle

This is the second paper in a series to discuss the approximation efficacy of polynomial interpolation of functions. In particular, the approximation accuracy depends sensitively on the locations of the interpolation nodes. We address the problem of finding the optimal symmetrical polynomial interpolation schemes for the triangle. The table for the symmetrical mean minimal interpolation sets for the triangle is given in this paper. An adaptive scheme for determining the interpolation order is also presented.