Recent Results for Moving Least Squares Approximation

We describe two experiments recently conducted with the approximate moving least squares (MLS) approximation method. On the one hand, the NFFT library of Kunis, Potts, and Steidl is coupled with the approximate MLS method to obtain a fast and accurate multivariate approximation method. The second experiment uses approximate MLS approximation in combination with a multilevel approximation algorithm. This method can be used for data compression, or to obtain an approximation with radial functions that employs variable scales and non-uniform center locations. §