In the present paper an iterative method is proposed
to approximate Moore-Ponrose and Drazin inverses. This method
is based on Global Least Square algorithm (GL-LSQR). To do so,
we define some linear matrix equations systems. By using the
approximate solutions of these systems, obtained by GL-LSQR algorithm, Moore-Ponrose and Drazin inverses are approximated.
Finally, some numerical examples are given to show the efficiency
of the new method.