Approximate moving least-squares approximation with compactly supported radial weights

We use Maz'ya and Schmidt's theory of approximate approximation to devise a fast and accurate approximate moving least-squares approximation method which does not require the solution of any linear systems. Since we use compactly supported weight functions, the remaining summation is also efficient. We compare our new algorithm with three other approximation methods based on compactly supported radial functions: multilevel interpolation, the standard moving least-squares approximation method, and a multilevel moving least-squares algorithm. A multilevel approximate moving least-squares approximation algorithm is also included.