Recurrent neural network for computing the W-weighted Drazin inverse

Two gradient based recurrent neural networks (RNNs) for computing the W-weighted Drazin inverse of a real rectangular matrix are proposed and considered. Usage of the first RNN is limited by a specific constraint on the spectrum of a certain matrix. The second RNN is usable without restrictions. The stability of the recurrent neural networks as well as their convergence are considered. Numerical examples are given to show the efficiency of the proposed neural networks.