Convergence Properties Analysis of Gradient Neural Network for Solving Online Linear Equations

A gradient neural network (GNN) for solving online a set of simultaneous linear equations is generalized and investigated in this paper. Instead of the earlier-presented asymptotical convergence, global exponential convergence could be proved for such a class of neural networks. In addition, superior convergence could be achieved using power-sigmoid activation-functions, compared with using linear activation-functions. Computer-simulation results substantiate further the above analysis and efficacy of such neural networks.