Restarted weighted full orthogonalization method for shifted linear systems

It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual method (GMRES) in several circumstances for solving shifted linear systems when the shifts are handled simultaneously. On the basis of the Weighted Arnoldi process, a weighted version of the Restarted Shifted FOM is proposed, which can provide accelerating convergence rate with respect to the number of restarts. In the cases where our hybrid algorithm needs less enough number of restarts to converge than the Restarted Shifted FOM, the associated CPU consuming time is also reduced, as shown by the numerical experiments. Moreover, our algorithm is able to solve certain shifted systems which the Restarted Shifted FOM cannot handle sometimes.