Augmented and deflated CMRH method for solving nonsymmetric linear systems

The CMRH (Changing Minimal Residual method based on the Hessenberg process) is an iterative method for solving nonsymmetric linear systems. The method generates a Krylov subspace in which   an approximate solution is determined.  The CMRH method is generally used with restarting to reduce the storage. Restarting often slows down the convergence.  In this paper we present  augmentation and deflation techniques for  accelerating  the convergence of the restarted CMRH method.  Augmentation adds a subspace to the Krylov subspace, while deflation removes certain parts from the operator.  Numerical experiments show that the new algorithms can be  more efficient compared with CMRH method.