Two improvements of the iterative method for computing Moore–Penrose inverse based on Penrose equations

Two improvements of the iterative method for computing the Moore–Penrose inverse, introduced in Petković and Stanimirović (2011) are introduced. The first improvement defines new choice for the initial approximation and ensures better stability of the method. The second one defines its extension to the set of outer inverses with prescribed range and null space. Numerical examples for both of these improvements are presented.