| Popis: |
The present paper is a contribution to data reduction in the multivariate case. In this direction, there are quite a few methods like ours dealing with scattered data points. Besides piecewise polynomial splines, radial basis functions (RBF splines) provide another natural generalization of univariate splines. Considering a set A of distinct scattered data points and a given tolerance c, our aim is to extract a subset A ⊂ A such that the RBF spline σ A stays within a tolerance A from the RBF spline σ A built upon the entire set A of data points. We show that for the usual RBF splines, data reduction can be considered from two different points of view: a priori reduction which amounts to adding nodes one after the other, starting from a small subset of A, thus refering to a rough approximation of σ A , and a posteriori reduction, which in contrast consists of deleting nodes one after the other from the ultimate spline σ A |
