Neural network approach to computing outer inverses based on the full rank representation

The first intention of this paper is to emphasize equivalence between two well known general representations of outer inverses with prescribed range and null space of a given matrix. Two dynamical state equations, corresponding to particular expressions which are included in these representations, are defined within the second objective. In this way, two gradient based neural networks, initiated by introduced dynamical equations, are exploited in generating the class of outer inverses. The results corresponding to most common generalized inverses are obtained in particular cases. Numerical results are presented.