TY - GEN A1 - Mehrmann, Volker A1 - Poloni, Federico T1 - Doubling Algorithms With Permuted Lagrangian Graph Bases N2 - We derive a new representation of Lagrangian subspaces in the form % \[ {\mathrm Im}\Pi^T [I,X]^T, \] % where $\Pi$ is a symplectic matrix which is the product of a permutation matrix and a real orthogonal diagonal matrix, and $X$ satisfies % \[ \abs{X_{ij}} \leq \begin{cases}1 & \text{if $i=j$,}\\ \sqrt{2} & \text{if $i\neq j$.} \end{cases} \] % This representation allows 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. KW - Lagrangian subspace KW - optimal control KW - structure-preserving doubling algorithm KW - symplectic matrix KW - Hamiltonian matrix KW - matrix pencil KW - graph subspace Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/906 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-9067 ER -