## Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations

- Tayyebe Haqiri, Federico Poloni
- J. Computational Applied Mathematics
- 2017

2 Excerpts

- Published 2012 in SIAM J. Matrix Analysis Applications

We derive a new representation of Lagrangian subspaces in the form ImΠT [ I X ] , where Π is a symplectic matrix which is the product of a permutation matrix and a real orthogonal diagonal matrix, and X satisfies |Xij | ≤ { 1 if i = j, √ 2 if i = j. This representation allows us to limit element growth in the context of doubling algorithms for the computation of Lagrangian subspaces and the solution of Riccati equations. It is shown that a simple doubling algorithm using this representation can reach full machine accuracy on a wide range of problems, obtaining invariant subspaces of the same quality as those computed by the state-of-the-art algorithms based on orthogonal transformations. The same idea carries over to representations of arbitrary subspaces and can be used for other types of structured pencils.

@article{Mehrmann2012DoublingAW,
title={Doubling Algorithms with Permuted Lagrangian Graph Bases},
author={Volker Mehrmann and Federico Poloni},
journal={SIAM J. Matrix Analysis Applications},
year={2012},
volume={33},
pages={780-805}
}