A Theoretical Comparison of the Arnoldi and GMRES Algorithms

@article{Brown1991ATC,
  title={A Theoretical Comparison of the Arnoldi and GMRES Algorithms},
  author={Peter N. Brown},
  journal={SIAM J. Scientific Computing},
  year={1991},
  volume={12},
  pages={58-78}
}
Two recently developed Krylov methods for solving linear systems are Arnoldi’s method and the Generalized Minimum Residual (GMRES) method. The GMRES method has been considered superior to Arnoldi’s method due in part to the fact that GMRES never breaks down in the way Arnoldi’s algorithm can. However, it is shown that there is a relationship between breakdowns in the two methods. Specifically, it is shown that GMRES does exhibit breakdowns very similar to that of Arnoldi, often referred to as… CONTINUE READING

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