Summary: The numerical computation of Lagrangian invariant subspaces of large-scale Hamiltonian matrices is discussed in the context of the solution of Lyapunov equations. A new version of the low-rank alternating direction implicit method is introduced, which, in order to avoid numerical difficulties with solutions that are of very large norm, uses an inverse-free representation of the subspace and avoids inverses of ill-conditioned matrices. It is shown that this prevents large growth of the elements of the solution that may destroy a low-rank approximation of the solution. A partial error analysis is presented, and the behavior of the method is demonstrated via several numerical examples. Copyright

An inverse-free ADI algorithm for computing Lagrangian invariant subspaces

POLONI, FEDERICO GIOVANNI
2016-01-01

Abstract

Summary: The numerical computation of Lagrangian invariant subspaces of large-scale Hamiltonian matrices is discussed in the context of the solution of Lyapunov equations. A new version of the low-rank alternating direction implicit method is introduced, which, in order to avoid numerical difficulties with solutions that are of very large norm, uses an inverse-free representation of the subspace and avoids inverses of ill-conditioned matrices. It is shown that this prevents large growth of the elements of the solution that may destroy a low-rank approximation of the solution. A partial error analysis is presented, and the behavior of the method is demonstrated via several numerical examples. Copyright
2016
Mehrmann, Volker; Poloni, FEDERICO GIOVANNI
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/775263
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