Surfaces generated by moving least squares methods

TLDR

Moving least squares methods are projection-based processes whose compositions exhibit specific properties. The paper presents moving least squares methods for smoothing and interpolating scattered data. The authors analyze moving least squares projectors, including those linked to finite element schemes, to smooth and interpolate scattered data. The analysis proves theorems on the smoothness of moving least squares interpolants, describes them as projection methods, and illustrates the results with univariate and bivariate examples.

Abstract

An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analysis is accompanied by examples of univariate and bivariate problems.