Geodesic
Perturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations
The electronic journal of linear algebra, Tome 17 (2008), pp. 234-257.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The perturbation theory for purely imaginary eigenvaluesof Hamiltonian matrices under Hamiltonian and non-Hamiltonian perturbations is discussed. It is shown that there is a substantial difference in the behavior under these perturbations. The perturbation of real eigenvalues of real skew-Hamiltonian matrices under structured perturbations is discussed as well and these results are used to analyze the properties of the URV method for computing the eigenvalues of Hamiltonian matrices.
Classification : 15A18, 15A57, 65F15, 65F35
Keywords: Hamiltonian matrix, skew-Hamiltonian matrix, symplectic matrix, structured perturbation, invariant subspace, purely imaginary eigenvalues, passive system, robust control, gyroscopic system 
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     author = {Mehrmann, Volker and Xu, Hongguo},
     title = {Perturbation of purely imaginary eigenvalues of {Hamiltonian} matrices under structured perturbations},
     journal = {The electronic journal of linear algebra},
     pages = {234--257},
     publisher = {mathdoc},
     volume = {17},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2008__17__a27/}
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Mehrmann, Volker; Xu, Hongguo. Perturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations. The electronic journal of linear algebra, Tome 17 (2008), pp. 234-257. http://geodesic.mathdoc.fr/item/ELA_2008__17__a27/