The Solution of Approximation Problems on RBF Networks Learned by The Levenberg Marquardt Method

A promising tool for solving problems of approximating functions, including problems of gridless approximation, is radial basis functions networks, which is a special type of neural networks. Since the solution of the problem has formed in the process of network learning, it is important to develop fast learning algorithms for networks. Currently, first-order gradient methods have used to learn radial basis functions networks. These methods have a low rate of convergence and practically do not allow to achieve high accuracy of approximation for complex functions. The article proposes to use the Levenberg-Marquardt method for learning the network in solving approximation problems. An algorithm for learning the network by the Levenberg-Marquardt method has developed. The algorithm takes into account the specifics of the architecture of networks of radial basis functions and uses analytical calculation of the elements of the Jacobi matrix. The effectiveness of the algorithm has confirmed by solving model problems.