Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Parallel iterative solvers for sparse linear systems in circuit simulation
Future Generation Computer Systems
Parallel iterative solvers for sparse linear systems in circuit simulation
Future Generation Computer Systems
Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Flexible global generalized Hessenberg methods for linear systems with multiple right-hand sides
Journal of Computational and Applied Mathematics
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A flexible version of the QMR algorithm is presented which allows for the use of a different preconditioner at each step of the algorithm. In particular, inexact solutions of the preconditioned equations are allowed, as well as the use of an (inner) iterative method as a preconditioner. Several theorems 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 GMRES (FGMRES). In addition, numerical experiments are presented which illustrate the convergence of flexible QMR (FQMR), and show that in certain cases FQMR can produce approximations with lower residual norms than QMR.