Doubling Algorithms with Permuted Lagrangian Graph Bases

@article{Mehrmann2012DoublingAW,
  title={Doubling Algorithms with Permuted Lagrangian Graph Bases},
  author={Volker Mehrmann and Federico Poloni},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2012},
  volume={33},
  pages={780-805}
}
We derive a new representation of Lagrangian subspaces in the form ${\rm Im} \Pi^T\big[\begin{smallmatrix}I \\ X\end{smallmatrix}\big]$, where $\Pi$ is a symplectic matrix which is the product of a permutation matrix and a real orthogonal diagonal matrix, and $X$ satisfies $\left\vert X_{ij}\right\vert \leq \begin{cases}1 & \text{if $i=j$,}\\ \sqrt{2} & \text{if $i\neq j$.} \end{cases}$ This representation allows us to limit element growth in the context of doubling algorithms for the… 

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