On Best Approximation of the Monomials on the Unit Ball of Rr Original Research Article

Bos and Liang have separately proved that the Kergin interpolants with respect to distinguished nodes on the unit disk are best approximations of the monomials in the infinity norm. These results are extended by characterizing the nodes as solutions of a system of nonlinear equations. Thus, it is possible to get all nodes with this property on the unit disk and it is likewise possible to lift results to the ball in the sense of approximation in the mean.