A two-step algorithm for solving singular linear systems with index one Jieyong Zhou a,1 , Yimin Wei b, * ,2 a Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, PR China b Department of Mathematics, Fudan University, Shanghai 200433, PR China Abstract 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. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Iterative methods; DGMRES; Two-step algorithm; Singular linear system; Drazin inverse; Index 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.07.027 * Corresponding author. E-mail addresses: yehangch@yahoo.com.cn (J. Zhou), ymwei@fudan.edu.cn (Y. Wei). 1 Also a postdoctor working at Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, PR China. 2 Supported by National Natural Science Foundation of China under grant 10471027 and Shanghai Education Committee. Applied Mathematics and Computation 175 (2006) 472–485 www.elsevier.com/locate/amc