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Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices |
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| Authors: | Peter Benner Volker Mehrmann Hongguo Xu |
| Institution: | (1) Zentrum für Technomathematik, Fachbereich 3/Mathematik und Informatik, Universität Bremen, D-28334 Bremen, Germany;(2) Fakultät II für Mathematik und Naturwissenschaften, Institut für Mathematik, MA 4-5, Technische Universität Berlin, Str. des 17. Juni 136, D-10623 Berlin, Germany;(3) Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA |
| Abstract: | We study the perturbation theory for the eigenvalue problem of a formal matrix product A
1
s
1 ··· A
p
s
p, where all A
k are square and s
k  {–1, 1}. We generalize the classical perturbation results for matrices and matrix pencils to perturbation results for generalized deflating subspaces and eigenvalues of such formal matrix products. As an application we then extend the structured perturbation theory for the eigenvalue problem of Hamiltonian matrices to Hamiltonian/skew-Hamiltonian pencils. |
| Keywords: | Perturbation theory eigenvalue problem formal matrix products periodic QZ algorithm Hamiltonian matrix skew-Hamiltonian matrix deflating subspace |
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