BIT Numerical Mathematics

, Volume 50, Issue 1, pp 207–220 | Cite as

A note on preconditioned GMRES for solving singular linear systems

  • Naimin Zhang


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.

Singular linear systems Range-symmetric Proper splitting Singular perconditioner 

Mathematics Subject Classification (2000)

15A09 65F10 


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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceWenzhou UniversityWenzhouChina

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