Peter Benner, Daniel Kressner

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.

Article

Peter Benner,
Daniel Kressner,
et al.
" Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II."
*ACM Transactions on Mathematical Software*.
doi:10.1145/1141885.1141895.
Retrieved 02/26/2021 from researchcompendia.org/compendia/2013.293/

**Compendium Type**: Published Papers

**Primary Research Field**: Computer and Information Sciences

**Secondary Research Field**: Mathematics

**Content License**: Public Domain Mark

**Code License**: MIT License

created 12/12/2013

modified 01/16/2014

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