A note on preconditioned GMRES for solving singular linear systems

Abstract

For solving a singular linear system Ax = b by GMRES, it is shown in the literature that if A is range-symmetric, then GMRES converges safely to a solution. In this paper we consider preconditioned GMRES for solving a singular linear system, we construct preconditioners by so-called proper splittings, which can ensure that the coefficient matrix of the preconditioned system is range-symmetric. © Springer Science + Business Media B.V. 2009.