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SHHEIG: Routines for Skew-Hamiltonian/Hamiltonian Eigenvalue Problems

Several FORTRAN 77 routines for the structure-preserving treatment of generalized eigenvalue problems with skew-Hamiltonian/Hamiltonian structure. The algorithms which are used base on the embedding of the skew-Hamiltonian/Hamiltonian matrix pencil λS-H into a matrix pencil of double dimension in order to ensure the existence of a structured Schur form. The implemented routines can be in particular used for

  • the computation of the eigenvalues of λS-H (via generalized symplectic URV decomposition),
  • the computation of certain condensed forms (in particular the structured Schur forms of the embedded matrix pencils),
  • eigenvalue reordering,
  • the computation of the stable deflating subspaces.

There exist both codes for real and complex problems with variants for factored and unfactored matrices S, respectively. Moreover, MEX files have been developed which enable a direct call from Matlab.

sHHeigspic.jpg

Computed eigenvalues of the new method compared with those of the QZ algorithm for the stability analysis of a gyroscopic system

Authors

  • Vasile Sima (National Institute for Research & Development in Informatics, Bucharest, Romania)
  • Matthias Voigt (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg)

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This software underlies the ACM Software Copyright and License Agreement. If you use this code for your own work, then please cite the publications stated below.

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