A two-step algorithm for solving singular linear systems with index one

In this paper, a two-step algorithm for solving singular linear systems is presented. We compare this algorithm with a DGCR type algorithm [A. Sidi, A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular non-symmetric linear systems, Linear Algebra Appl. 298 (1999) 99–113] by numerical experiments. An error analysis is given.