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Numerische Mathematik

, Volume 78, Issue 3, pp 329–358 | Cite as

A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils

  • Peter Benner
  • Volker Mehrmann
  • Hongguo Xu

Abstract.

A new method is presented for the numerical computation of the generalized eigenvalues of real Hamiltonian or symplectic pencils and matrices. The method is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order \(\sqrt{\varepsilon}\), where \(\varepsilon \) is the machine precision, the new method computes the eigenvalues to full possible accuracy.

Mathematics Subject Classification (1991):65F15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Peter Benner
    • 1
  • Volker Mehrmann
    • 2
  • Hongguo Xu
    • 3
  1. 1. Zentrum für Technomath, Fb 3 – Mathematik und Informatik, Universität Bremen, Postfach 330 440, D-28334 Bremen, Germany; e-mail: benner@numerik.uni-bremen.de DE
  2. 2. Fakultät für Mathematik, TU Chemnitz, D-09107 Chemnitz, Germany; e-mail: mehrmann@mathematik.tu-chemnitz.de DE
  3. 3. Department of Mathematics, Fudan University, Shanghai, 200433, PR China CN

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