Moving Least Squares via Orthogonal Polynomials

A method for moving least squares interpolation and differentiation is presented in the framework of orthogonal polynomials on discrete points. This yields a robust and efficient method which can avoid singularities and breakdowns in the moving least squares method caused by particular configurations of nodes in the system. The method is tested by applying it to the estimation of first and second derivatives of test functions on random point distributions. The effect of singular point configurations is illustrated with respect to their effect on the accuracy and convergence of the estimated derivatives.