A matrix decomposition RBF algorithm: Approximation of functions and their derivatives

We propose an efficient algorithm for the approximation of functions and their derivatives using radial basis functions (RBFs). The interpolation points are placed on concentric circles and the resulting matrix has a block circulant structure. We exploit this circulant structure to develop an efficient algorithm for the solution of the resulting system using RBFs. As a result, extremely high accuracy in approximating the given function and its derivatives can be achieved. The given algorithm is also capable of solving large-scale problems with more than 100 000 interpolation points in two dimensions.