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}\cite{dub}. 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.
Sets of Near-Optimal Points for Interpolation on the Square
DE MARCHI, Stefano
2005-01-01
Abstract
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}\cite{dub}. 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.
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