On the Convergence of General Stationary Linear Iterative Methods for Singular Linear Systems

Abstract

Recently, Lee et al. have published an interesting paper [SIAM J. Matrix Anal. Appl., 28 (2006), pp. 634–641] concerning the energy norm convergence of general stationary linear iterative methods for semidefinite linear systems. In this paper, we first consider the convergence of general stationary linear iterative methods for general singular consistent linear systems and show that the convergence and the quotient convergence are equivalent. Then we consider the convergence of general stationary iterative methods for the semidefinite systems and clarify some issues in Lee et al.'s paper.