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

DGMRES method augmented with eigenvectors for computing the Drazin-inverse solution of singular linear systems