Successive matrix squaring algorithm for computing outer inverses

In this paper, we derive a successive matrix squaring (SMS) algorithm to approximate an outer generalized inverse with prescribed range and null space of a given matrix A∈Crm×n. We generalize the results from the papers [L. Chen, E.V. Krishnamurthy, I. Macleod, Generalized matrix inversion and rank computation by successive matrix powering, Parallel Computing 20 (1994) 297–311; Y. Wei, Successive matrix squaring algorithm for computing Drazin inverse, Appl. Math. Comput. 108 (2000) 67–75; Y. Wei, H. Wu, J. Wei, Successive matrix squaring algorithm for parallel computing the weighted generalized inverse AMN†, Appl. Math. Comput. 116 (2000) 289–296], and obtain an algorithm for computing various classes of outer generalized inverses of A  . Instead of particular matrices used in these articles, we use an appropriate matrix R∈Csn×m, s⩽rs⩽r. Numerical examples are presented.