An Adaptive Method for Choosing Center Sets of RBF Interpolation

Radial basis functions (RBF) provide powerful meshfree methods for multivariate interpolation for scattered data. RBF methods have been praised for their simplicity and ease of implementation in multivariate scattered data approximation. But both the approximation quality and stability depend on the distribution of the center set. It leads immediately to the problem of finding good or even optimal point sets for the reconstruction process. Many methods are constructed for center choosing. In this paper, we give a short overview of these algorithms including thinning algorithm, greedy algorithm, arclength equipartition like algorithm and k-means clustering algorithm. A new adaptive data-dependent method is provided at the end with some numerical examples to show its effectiveness..