A spectral trichotomy method for symplectic matrices

@article{Dosso2009AST,
  title={A spectral trichotomy method for symplectic matrices},
  author={Mouhamadou Dosso and Miloud Sadkane},
  journal={Numerical Algorithms},
  year={2009},
  volume={52},
  pages={187-212}
}
This paper presents an algorithm for the numerical approximation of spectral projectors onto the invariant subspaces corresponding to the eigenvalues inside, on, and outside the unit circle of a symplectic matrix. The algorithm constructs iteratively three matrix sequences from which the projectors are obtained. The convergence depends essentially on the gap between the unit circle and the eigenvalues inside it. A larger gap leads to faster convergence. Theoretical and algorithmic aspects of… CONTINUE READING