Recurrent neural networks for computing weighted Moore-Penrose inverse

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.

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