Recurrent Neural Networks for Coupled Matrix Equations Based on Gradient Search

A gradient-based neural network is investigated and analyzed for coupled matrix equations. First, a non-negative function is established to construct the neural network. Then, a recurrent neural network is developed to find the solution of coupled matrix equations. Some convergence results of the presented gradient-based neural network under different activation functions are developed. Moreover, a modified version of the designed neural network is proposed for the considered equations. Numerical examples are given to show the advantages of the developed methods.