DGMRES method augmented with eigenvectors for computing the Drazin-inverse solution of singular linear systems
For researchers working on iterative methods for singular linear systems, this work provides an incremental improvement to the DGMRES method by adapting an existing augmentation technique.
The authors address stagnation in the restarted DGMRES method for solving Drazin-inverse solutions of singular linear systems by augmenting the subspace with eigenvectors, demonstrating improved convergence through numerical examples.
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.