An oblique projection iterative method to compute Drazin inverse and group inverse

In this paper, an oblique projection iterative method is presented to compute matrix equation AXA=A of a square matrix A with ind(A)=1. By this iterative method, when taken the initial matrix X0=A, the group inverse Ag can be obtained in absence of the roundoff errors. If we use this iterative method to the matrix equation AkXAk=Ak, a group inverse (Ak)g of matrix Ak is got, then we use the formulae Ad=Ak-1(Ak)g, the Drazin inverse Ad can be obtained.