Iterated Approximate Moving Least Squares Approximation

The radial basis function interpolant is known to be the best approximation to a set of scattered data when the error is measured in the native space norm. The approximate moving least squares method, on the other hand, was recently proposed as an efficient approximation method that avoids the solution of the system of linear equations associated with the radial basis function interpolant. In this paper we propose and analyze an algorithm that iterates on the residuals of an approximate moving least squares approximation. We show that this algorithm yields the radial basis interpolant in the limit. Supporting numerical experiments are also included.