Global simpler GMRES for nonsymmetric systems with multiple right-hand sides

A new version of the simpler GMRES for solving nonsymmetric linear system of equations with multiple right-hand sides is presented. The main advantage over the simpler block GMRES is that the new method requires less storage and computational work per cycle. Preconditioning techniques can also be used to further accelerate the convergence of the new method. Finally, numerical examples are given to illustrate the effectiveness of the proposed method and its some preconditioned versions.