Spherical data fitting by multiscale moving least squares

This paper focuses on the multiscale moving least squares approximation scheme on the unit sphere, where the scale depends on the current evaluation points. The scheme is constructed by using a sequence of scaled weight functions, and is a little different from the classical moving least squares approximation on the sphere, which can be obtained by restricting compactly supported radial basis functions in R3 to S2. More precisely, a multiscale moving least squares (MMLS) algorithm, in which the corresponding scale is changing with the associated given point set, is proposed. In addition, the convergence analysis for the multiscale scheme and some numerical experiments to illustrate the theoretical results are given.