Ivan P. Stanimirović

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

Abstract An efficient algorithm for computing A T , 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.

Computation of generalized inverses by using the LDL∗ decomposition

An efficient algorithm, based on the LDL∗ factorization, for computing {1,2,3} and {1,2,4} inverses and the Moore–Penrose inverse of a given rational matrix A, is developed. We consider matrix products A∗A and AA∗ and corresponding LDL∗ factorizations in order to compute the generalized inverse of A. By considering the matrix products (R∗A)†R∗ and T∗(AT∗)†, where R and T are arbitrary rational matrices with appropriate dimensions and ranks, we characterize classes A{1,2,3} and A{1,2,4}. Some evaluation times for our algorithm are compared with corresponding times for several known algorithms for computing the Moore–Penrose inverse.