APPROXIMATION OF MULTIDIMENSIONAL FUNCTIONS BY RADON RADIAL BASIS NEURAL NETWORKS

The main result of this paper is to present a new method to approximate multidimensional function by using Radial Basis Neural Network with application of Radon Transform, and its inverse, to reduce the dimension of the space. This method consist of four stages: First, by using the Radon Transform, the multidimensional function can be reduced to several simpler one dimensional functions. Second, each of the one dimensional functions is approximated by using neural network technique into neural subnetworks. Third, these neural subnetworks are combined together to form the final approximation neural network. Four, using the inverse of Radon Transform to this final approximation neural network to get the approximation to the given function. Also, in this paper presenting a suitable adjusting to the parameters of the method to reduce the L2 approximate error. Also, we apply the above method to an example and a comparison is made with those in [2], and our numerical results are superior to those in [2].