Restarted GMRES for Shifted Linear Systems

@article{Frommer1998RestartedGF,
  title={Restarted GMRES for Shifted Linear Systems},
  author={Andreas Frommer and Uwe Gl{\"a}ssner},
  journal={SIAM J. Scientific Computing},
  year={1998},
  volume={19},
  pages={15-26}
}
Shifted matrices, which differ by a multiple of the identity only, generate the same Krylov subspaces with respect to any fixed vector. This fact has been exploited in Lanczos-based methods like CG, QMR, and BiCG to simultaneously solve several shifted linear systems at the expense of only one matrix–vector multiplication per iteration. Here, we develop a variant of the restarted GMRES method exhibiting the same advantage and we investigate its convergence for positive real matrices in some… CONTINUE READING

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