A flexible CMRH algorithm for nonsymmetric linear systems

A flexible version of the CMRH algorithm is presented that allows varying preconditioning at every step of the algorithm. A consequence of the flexibility of this new variant is that any iterative methods can be incorporated as a preconditioner in the inner steps. Theoretical results that relate the residual norm of the new algorithm and the flexible GMRES, the new algorithm with CMRH itself, are given. Numerical experiments are carried out to illustrate the effectiveness of the proposed algorithm in comparison with the standard CMRH algorithm, ILU-preconditioned CMRH variants and the flexible GMRES algorithm.