DQGMRES: a Direct Quasi-minimal Residual Algorithm Based on Incomplete Orthogonalization

We describe a Krylov subspace technique, based on incomplete or-thogonalization of the Krylov vectors, which can be considered as a truncated version of GMRES. Unlike GMRES(m), the restarted version of GMRES, the new method does not require restarting. Our numerical experiments show that DQGMRES method often performs better than GMRES(m). In addition, the algorithm is exible to variable preconditioning, i.e., it can accommodate variations in the precon-ditioner at every step. In particular, this feature allows us to use any iterative solver as a right-preconditioner for DQGMRES. This inner-outer iterative combination often results in a robust approach for in-deenite linear problems.