APPROXIMATION OF MULTIDIMENSIONAL FUNCTIONS BY RADON RADIAL BASIS NEURAL NETWORKS

Abstract

The main result of this paper is to present a new method to approximate multidimensionalfunction by using Radial Basis Neural Network with application of Radon Transform, and itsinverse, to reduce the dimension of the space. This method consist of four stages: First, by using theRadon Transform, the multidimensional function can be reduced to several simpler one dimensionalfunctions. Second, each of the one dimensional functions is approximated by using neural networktechnique into neural subnetworks. Third, these neural subnetworks are combined together to formthe final approximation neural network. Four, using the inverse of Radon Transform to this finalapproximation neural network to get the approximation to the given function. Also, in this paperpresenting 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], andour numerical results are superior to those in [2].