Applications of the hyper-power method for computing matrix products

We introduce representations for {1, 2, 3}, {1, 2, 4}-inverses in terms of matrix products involving the Moore-Penrose inverse. We also use representations of {2, 3} and {2, 4}-inverses of a prescribed rank introduced in [6] and [9]. These representations can be computed by means of the modification of the hyper-power iterative process which is used in computing matrix products involving the Moore-Penrose inverse, introduced in [8]. Introduced methods have arbitrary high orders q ≥ 2. A few comparisons with the known modification of the hyper-power method from [17] are presented.