Computation of generalized inverses by using the decomposition

An efficient algorithm, based on the L D L ∗ 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 A A ∗ and corresponding L D L ∗ factorizations in order to compute the generalized inverse of A . By considering the matrix products ( R ∗ A ) † R ∗ and T ∗ ( A T ∗ ) † , 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.