The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs

@article{Chu2011TheRM,
  title={The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs},
  author={Eric King-Wah Chu and Hung-Yuan Fan and Zhongxiao Jia and Tie-xiang Li and Wen-Wei Lin},
  journal={J. Computational Applied Mathematics},
  year={2011},
  volume={235},
  pages={2626-2639}
}
We extend the Rayleigh-Ritz method to the eigen-problem of periodic matrix pairs. Assuming that the deviations of the desired periodic eigenvectors from the corresponding periodic subspaces tend to zero, we show that there exist periodic Ritz values that converge to the desired periodic eigenvalues unconditionally, yet the periodic Ritz vectors may fail to converge. To overcome this potential problem, we minimize residuals formed with periodic Ritz values to produce the refined periodic Ritz… CONTINUE READING

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