Recurrent neural networks for computing weighted Moore–Penrose inverse

Abstract

Three recurrent neural networks are presented for computing the weighted Moore–Penrose inverse of rank-deficient matrices. The first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of weighted Moore–Penrose inverse under the condition of zero initial states. The second recurrent neural network consists of an array of neurons corresponding to a weighted Moore–Penrose inverse matrix with decaying self-connections and constant connections in each row or column. The third recurrent neural network consists of two layers of neuron arrays corresponding, respectively, to a weighted Moore–Penrose inverse and a Lagrangian matrix with constant connections.