Gradient neural dynamics for solving matrix equations and their applications.

We are concerned with the solution of the matrix equation A X B = D in real time by means of the gradient based neural network (GNN) model, called GNN ( A, B, D ). The convergence analysis shows that the result of global asymptotic convergence is determined by the choice of the initial state and coincides with the general solution of the matrix equation A X B = D . Several applications of the GNN ( A, B, D ) model in online approximation of various inner and outer inverses with prescribed range and/or null space are considered. An appropriate adaptation of proposed models for finding an online solution of a set of linear equations A x = b is defined and investigated. The influence of various nonlinear activation functions on the convergence of GNN ( A, B, D ) is investigated both theoretically as well as using computer-simulation results. [ABSTRACT FROM AUTHOR]