Firstly, we present new sets of nodes for polynomial interpolation on the square that are asymptotically distributed w.r.t. the Dubiner metrics 8 . 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 nonpolynomial case with radial basis functions we also present two families of nearlyoptimal interpolation points which can be determined independently of the radial function.

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... ne of these families can be conceptually described as a Leja sequence in the bivariate case.