Doubling Algorithms With Permuted Lagrangian Graph Bases

Please always quote using this URN:urn:nbn:de:0296-matheon-9067
  • 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.

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Metadaten
Author:Volker Mehrmann, Federico Poloni
URN:urn:nbn:de:0296-matheon-9067
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/10/20
Release Date:2011/10/20
Tag:
Institute:Technische Universität Berlin
Project:C Energy and Materials (Production)
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F05 Direct methods for linear systems and matrix inversion
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra
Preprint Number:821
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