Gradient Neural Network with Nonlinear Activation for Computing Inner Inverses and the Drazin Inverse

摘要

Two gradient-based recurrent neural networks (GNNs) for solving two matrix equations are presented and investigated. These GNNs can be used for generating various inner inverses, including the Moore–Penrose, and in the computation of the Drazin inverse. Convergence properties of defined GNNs are considered. Certain conditions which impose convergence towards the pseudoinverse, and the Drazin inverse are exactly specified. The influence of nonlinear activation functions on the convergence performance of defined GNN models is investigated. Computer simulation experience further confirms the theoretical results.