Parallel solution of a linear system using an SOR neural network

Successive over-relaxation (SOR) can be an efficient iterative method of solving linear systems of equations. However, parallel implementation depends on an appropriate structure in the coefficient matrix; for systems arising from discretization of the Poisson equation, a red-black ordering of the unknowns is suitable. One difficulty in utilizing SOR is the necessity of choosing a good value for the relaxation parameter, ω. We present a neural network for solving the Poisson equation applied to electrostatics. The neural network learns a good value for ω as it solves the linear system. The algorithm is based on the standard parallel SOR method. The performance of the sequential SOR and Jacobi methods are compared with the neural network for two sample problems