Lyapunov Inverse Iteration for Computing a Few Rightmost Eigenvalues of Large Generalized Eigenvalue Problems

@article{Elman2013LyapunovII,
  title={Lyapunov Inverse Iteration for Computing a Few Rightmost Eigenvalues of Large Generalized Eigenvalue Problems},
  author={Howard C. Elman and Minghao Wu},
  journal={SIAM J. Matrix Analysis Applications},
  year={2013},
  volume={34},
  pages={1685-1707}
}
In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special eigenvalue problem of Lyapunov structure. An analysis that explains the fast convergence of this… CONTINUE READING
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