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Main Title: An inverse-free ADI algorithm for computing Lagrangian invariant subspaces
Author(s): Mehrmann, Volker
Poloni, Federico
Type: Research Paper
Abstract: The numerical computation of Lagrangian invariant subspaces of large scale Hamiltonian matrices is discussed in the context of the solution of Lyapunov and Riccati 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 which 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.
Subject(s): Lagrangian subspace
permuted Lagrangian subspace
Lyapunov equation
Riccati equation
low-rank ADI method
inverse-free arithmetic
permuted graph basis
Issue Date: 5-Aug-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F15 Eigenvalues, eigenvectors
65F50 Sparse matrices
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 14
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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