Gradient neural dynamics for solving matrix equations and their applications

We are concerned with the solution of the matrix equation AXB=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 AXB=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 Ax=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.