Algorithm 854

Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms which can lead to considerable accuracy and performance improvements. As a by-product, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness of the subroutines for several, practically relevant examples.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 14 articles )

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  1. Freitag, Melina A.; Spence, Alastair: A new approach for calculating the real stability radius (2014)
  2. Jia, Zhigang; Wei, Musheng; Ling, Sitao: A new structure-preserving method for quaternion Hermitian eigenvalue problems (2013)
  3. Mehrmann, Volker; Schröder, C.; Simoncini, Valeria: An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems (2012)
  4. Benner, Peter; Faßbender, Heike; Stoll, Martin: A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process (2011)
  5. Maehara, Takanori; Murota, Kazuo: A numerical algorithm for block-diagonal decomposition of matrix $*$-algebras with general irreducible components (2010)
  6. Mehrmann, V.; Schröder, C.; Watkins, D.S.: A new block method for computing the Hamiltonian Schur form (2009)
  7. Chu, Moody T.: Linear algebra algorithms as dynamical systems (2008)
  8. Benzi, Michele; Razouk, Nader: On the Iwasawa decomposition of a symplectic matrix (2007)
  9. Chu, Delin; Liu, Xinmin; Mehrmann, Volker: A numerical method for computing the Hamiltonian Schur form (2007)
  10. Watkins, David S.: On the reduction of a Hamiltonian matrix to Hamiltonian Schur form (2006)
  11. Benner, Peter; Kressner, Daniel; Mehrmann, Volker: Skew-Hamiltonian and Hamiltonian eigenvalue problems: theory, algorithms and applications (2005)
  12. Kressner, Daniel: Perturbation bounds for isotropic invariant subspaces of skew-Hamiltonian matrices (2005)
  13. Kreßner, Daniel: Numerical methods and software for general and structured eigenvalue problems. (2004)
  14. Benner, Peter; Byers, Ralph; Barth, Eric: Algorithm 800. Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices. I: The square-reduced method. (2000)