Two methods for computing the Drazin inverse through elementary row operations

Abstract

In this paper, Let the matrix A ∈ C n×n with Ind(A) = k, we first construct two bordered matrices based on [32], which gave a method for computing the null space of A k by applying elementary row operations on the pair A I. Then two new Algorithms to compute the Drazin inverse A d are presented based on elementary row operations on two partitioned matrices. The computational complexities of the two Algorithms are detailed analyzed. When the index k = Ind(A) ≥ 5, the two Algorithms are all faster than the Algorithm by Anstreicher and Rothblum [32]. In the end, an example is presented to demonstrate the two new algorithms.