Common Nature of Learning Exemplified by BP and Hopfield Neural Networks for Solving Online a System of Linear Equations

Many computational problems widely encountered in scientific and engineering applications could finally be transformed to the online linear-equations solving. Classic numerical methods for solving linear equations include Gaussian elimination and matrix factorization methods, which are usually of O(n³) operations. Being important parallel-computational models, both BP (back propagation) and Hopfield neural networks could be exploited for solving such linear equations. BP neural network is evidently different from Hopfield neural network in terms of network definition, architecture and learning pattern. However, both of these two neural networks could have a common nature of learning (i.e., governed by the same mathematical iteration formula) during the online solution of linear equations. In addition, computer-simulation results substantiate the theoretical analysis of both BP and Hopfield neural networks for solving online such a set of linear equations.