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

Andreas Karageorghis, C. S. Chen, Yiorgos-Sokratis Smyrlis

• 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.