An optimization network for solving a set of simultaneous linear equations

A network for solving systems of simultaneous linear equations based on Hopfield´s neural network model with continuous, real-valued outputs is described. The network is composed of highly interconnected simple neurons with a linear transfer function at each node. It is guaranteed to converge to a correct solution for all solvable systems of equations irrespective of the choice of the node transfer function; the use of complex nonlinearities at the nodes only affects the network convergence time. When a system which admits a solution is given as input, the network converges spontaneously and rapidly to a very accurate solution in all cases. When an unsolvable system is provided as input, the network outputs fail to converge and make the energy function close to zero even after a very large number of iterations