Adaptive greedy techniques for approximate solution of large RBF systems

Abstract

For the solution of large sparse linear systems arising from interpolation problems using compactly supported radial basis functions, a class of efficient numerical algorithms is presented. They iteratively select small subsets of the interpolation points and refine the current approximative solution there. Convergence turns out to be linear, and the technique can be generalized to positive definite linear systems in general. A major feature is that the approximations tend to have only a small number of nonzero coefficients, and in this sense the technique is related to greedy algorithms and best n-term approximation.