zbMATH — the first resource for mathematics

Approximate moving least-squares approximation with compactly supported radial weights. (English) Zbl 1014.65014
Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations. International workshop, Univ. Bonn, Germany, September 11-14, 2001. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 26, 105-116 (2002).
Summary: We use V. Maz’ya and G. Schmidt’s theory of approximate approximation [IMA J. Numer. Anal. 16, No. 1, 13-29 (1996; Zbl 0838.65005); J. Approximation Theory 110, No. 2, 125-145 (2001; Zbl 0976.41004)] 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.
For the entire collection see [Zbl 0996.00042].

65D10 Numerical smoothing, curve fitting
65D05 Numerical interpolation