  The DGMRES method for solving Drazin-inverse solution of singular linear
systems is generally used with restarting. But the restarting often slows down
the convergence and DGMRES often stagnates. We show that adding some
eigenvectors to the subspace can improve the convergence just like the method
proposed by R.Morgan in [R.Morgan, A restarted GMRES method augmented with
eigenvectors, SIAM J.Matrix Anal.Appl. 16 (1995)1154-1171]. We derive the
implementation of this method and present some numerical examples to show the
advantages of this method.
