Full-rank representations of outer inverses based on the QR decomposition

摘要

An efficient algorithm for computing AT,S(2) inverses of a given constant matrix A, based on the QR decomposition of an appropriate matrix W, is presented. Correlations between the derived representation of outer inverses and corresponding general representation based on arbitrary full-rank factorization are derived. In particular cases we derive representations of {2,4} and {2,3}-inverses. Numerical examples on different test matrices (dense or sparse) are presented as well as the comparison with several well-known methods for computing the Moore–Penrose inverse and the Drazin inverse.