Approximate Moving Least-Squares: 
A Fast and Accurate Meshless Method

Abstract

We combine ideas from the moving least-squares meshless approximation method, quasi-interpolation, and the theory of approximate approximations due to Maz'ya and Schmidt to develop a scattered data approximation method that can achieve arbitrarily high approximation orders coupled with a numerical precision which can be set by the user. An example of such a method is given by a radial discrete Laguerre transform. By borrowing from the field of fast multipole-like algorithms we are able to design a fast evaluation algorithm for the radial Laguerre transform.