Development of a Hopfield network for solving integral equations

Abstract

The authors present a novel strategy for solving integral equations using a Hopfield type network. The major advantage of this strategy is the guaranteed convergence to the globally optimum solution ensured by the causality property of the network and the continuous nature of the feedback to each node. The algorithm consists of deriving the two function minimization equations, one for the energy function of the network and the other for the least squares solution of the discretized integral equation with appropriate regularization conditions. By comparing similar terms of the two equations the circuit parameters of the network are estimated. The network is then simulated for obtaining the solution of the integral equation. Initial simulation results are presented.