Solution of a linear system using a neural network based on iterative techniques

similar to Successive Over Relaxation (SOR). The network is trained to find the appropriate relaxation parameter. A derivation of the algorithm and its relation to the SOR algorithm is given. The performance of the standard SOR and Jacobi methods are compared with the neural network for two sample problems. 1. INTRODUCTION A simple neural network with no hidden units and no nonlinearities (i.e. the identity function for its activation function) performs a vector-matrix multiplication. For the problem of solving a linear system, Ax=b (1)Iterative solutions of this system can be visualized as recurrent networks consisting of two levels. Theiterative algorithm). The second level corresponds to the calculation of the vector-matrix product which equals the given right hand side, b, when the solution process has converged. The standard Jacobi method can be expressed in terms of a neural network architecture easily. However, without the use ofany adjustable parameters, neural networks provide a parallel solution technique.The most common iterative solution technique for linear systems that utilizes a parameter whichmake a neural network architecture for this algorithm quite cumbersome. We have, therefore, developed