Full‐rank representations of {2,4}, {2,3}‐inverses and successive matrix squaring algorithm

We present the full‐rank representations of {2,4} and {2,3}‐inverses (with given rank as well as with prescribed range and null space) as particular cases of the full‐rank representation of outer inverses. As a consequence, two applications of the successive matrix squaring (SMS) algorithm from [P.S. Stanimirovic, D.S. Cvetkovic‐Ilic, Successive matrix squaring algorithm for computing outer inverses, Appl. Math. Comput. 203 (2008) 19–29] are defined using the full‐rank representations of {2,4} and {2,3}‐inverses. The first application is used to approximate {2,4}‐inverses. The second application, after appropriate modifications of the SMS iterative procedure, computes {2,3}‐inverses of a given matrix. Presented numerical examples clarify the purpose of the introduced methods.