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Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices

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Abstract

We study the perturbation theory for the eigenvalue problem of a formal matrix product A s1 1 ··· A sp 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.

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Authors and Affiliations

  1. Zentrum für Technomathematik, Fachbereich 3/Mathematik und Informatik, Universität Bremen, D-28334, Bremen, Germany

    Peter Benner

  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

    Volker Mehrmann

  3. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Hongguo Xu

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  1. Peter Benner
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  2. Volker Mehrmann
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Benner, P., Mehrmann, V. & Xu, H. Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices. BIT Numerical Mathematics 42, 1–43 (2002). https://doi.org/10.1023/A:1021966001542

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