GMRES-type methods for inconsistent systems Original Research Article

The behavior of iterative methods of GMRES-type when applied to singular, possibly inconsistent, linear systems is discussed and conditions under which these methods converge to the least-squares solution of minimal norm are presented. Error bounds for the computed iterates are shown. This paper complements previous work by Brown and Walker [P.N. Brown, H.F. Walker, SIAM J. Matrix Anal. Appl. 18 (1997) 37–51].