FQMR: A flexible quasi-minimal residual method with inexact preconditioning

A flexible version of the QMR algorithm is presented which allows for the u se of a different preconditioner at each step of the algorithm. In particul ar, inexact solutions of the preconditioned equations are allowed, as well as the use of an (inner) iterative method as a preconditioner. Several theo rems are presented relating the norm of the residual of the new method with the norm of the residual of other methods, including QMR and flexible GMRE S (FGMRES). In addition, numerical experiments are presented which illustra te the convergence of flexible QMR (FQMR), and show that in certain cases F QMR can produce approximations with lower residual norms than QMR.