Doubling Algorithms with Permuted Lagrangian Graph Bases


We derive a new representation of Lagrangian subspaces in the form ImΠ T 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 |X ij | ≤ 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.

DOI: 10.1137/110850773

Extracted Key Phrases

Showing 1-10 of 46 references

How to find a good submatrix

  • S A Goreinov, I V Oseledets, D V Savostyanov, E E Tyrtyshnikov, N L Zamarashkin
  • 2010
Highly Influential
1 Excerpt

Sensitivity analysis of the algebraic Riccati equations

  • S.-F Xu
  • 1996
Highly Influential
1 Excerpt

Best " local chart for an element of gr(n, 2n), MathOverflow, http://

  • D Speyer
  • 2011

The palindromic generalized eigenvalue problem A * x = λAx: Numerical solution and applications

  • T Li, C.-Y Chiang, E K Chu, W.-W Lin
  • 2011