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)(dagger)R* and T*(AT*)(dagger), 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. (C) 2011 Elsevier Ltd. All rights reserved.