Improved Convergence of Multilevel Moving Least-Squares Approximation

Abstract

Moving least-squares approximation is a popular method for approximating multivariate functions from given discrete data. For higher accuracy higher degree polynomials have to be used, resulting also in higher computational cost and numerical instabilities. Recently, the combination of low-order moving least squares with a multilevel scheme showed superior numerical behavior. In this paper we will prove, amongst other things, that such a combination of moving least-squares with a multilevel scheme indeed leads to improved convergence results, at least if the data sites form a regular grid.