On optimal center locations for radial basis interpolation: computational aspects

The problem of choosing “good” nodes is a central one in polynomial interpolation. Made curious from this problem, in this work we present some results concerning the computation of optimal points sets for interpolation by radial basis functions. Two algorithms for the construction of near-optimal set of points are considered. The first, that depends on the radial function, compute optimal points by adding one of the maxima of the power function with respect to the preceding set. The second, which is independent of the radial function, is shown to generate near-optimal sets which correspond to Leja extremal points. Both algorithms produce point sets almost similar, in the sense of their mutual separation distances. We then compare the interpolation errors and the growth of the Lebesgue constants for both point sets.