Numerical Experiments in Surface Approximation
by
Robert Schaback
Univ. Goettingen, Germany
Coauthors: Holger Wendland

For surface construction by radial basis functions from large sets of scattered data, we first look at the numerical behavior of iterative algorithms. Inspired by recent results of Faul & Powell we prove linear convergence of a modified algorithm. Numerical experiments with large systems show certain effects that should be investigated further, e.g. into the direction of multigrid/multilevel techniques. We show a series of examples and try to compare different techniques.

The second topic concerns choosing the proper scale of a compactly supported radial basis function when applied to interpolate a surface. Experiments show that there is good numerical support for multilevel techniques that are comparable to stationary methods on regular grids. Linear convergence with respect to the level index can be observed in many cases.

If time permits, we finally report on moving least squares approximations to surfaces. This will include a simple proof of an optimal approximation order and some numerical experiments.

http://www.num.math.uni-goettingen.de/schaback

Date received: December 16, 1998