Computing outer inverses by scaled matrix iterations

Convergence analysis for a class of iterative methods for computing outer inverses with prescribed range and null space is studied. Furthermore, several heuristics for accelerating iterative methods via scaling are proposed. In fact, we are motivated by the fact that scaling of iterative methods for computing generalized inverses is investigated so far only on low-order methods. Our intention is to test the scaling on higher-order iterative methods. Here, we also propose a new higher-order iteration. Although the introduced method is efficient in terms of computational efficiency index, we test its acceleration through several experiments.