Benner, PeterKressner, Daniel2011-05-052011-05-052011-05-05200610.1145/1141885.1141895https://infoscience.epfl.ch/handle/20.500.14299/67072This 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.algorithmsdocumentationperformancealgebraic Riccati equationeigenvaluesHamiltonian matrixinvariant subspacesskew-Hamiltonian matrixsymplectic QR decompositionStructure-Preserving MethodsLinear AlgebraNumerical-SolutionRiccati EquationFactorizationsStabilitySystemsPencilstext::journal::journal article::research article