Neural network for computing pseudoinverses and outer inverses of complex-valued matrices

We propose two continuous-time neural networks for computing generalized inverses of complex-valued matrices with rank-deficient cases. The first of them is applicable in the pseudoinverse computation and the second one is applicable in construction of outer inverses. The proposed continuous-time neural networks have a low complexity of implementation and they are proved to be globally convergent without any condition. Compared with the existing algorithms for computing the pseudoinverse and outer inverses of matrices, the global convergence of the proposed continuous-time neural networks is analyzed in the complex domain. Effectiveness of the proposed continuous-time neural networks is evaluated numerically via examples.