Sets of Near-Optimal Points for Interpolation on the Square

Firstly, we present new sets of nodes for {\em polynomial interpolation on the square} that are asymptotically distributed w.r.t. the {\em Dubiner metrics}. Then, we shall deal with two particular families which show Lebesgue constants that numerically grow like $\log^2(n)$, with $n$ the degree of the interpolating polynomial. In the non-polynomial case with {\em radial basis functions} we also present two families of nearly-optimal interpolation points which can be determined {\it independently} of the radial function. One of these families can be conceptually described as a {\em Leja sequence} in the bivariate case.