Software for (Skew-)Hamiltonian Eigenvalue Problems
The Hamiltonian Eigenvalue Problem is an important structured Eigenvalue Problem in Systems and Control theory. Through its close connection to the Riccati Matrix equation the Hamiltonian Eigenvalue Problem becomes one of the building blocks of the software development in our group. Over the past years we develop a set of FORTRAN 77 and MATLAB routines for the solution of the Hamiltonian Eigenvalue Problem. Beside them we focus on a set of benchmark problems for the Riccati equation which are suitable for the Hamiltonian Eigensolvers as well.
HAPACK is an LAPACK-style software package for Hamiltonian and skew-Hamiltonian matrices. It provides subroutines for computing eigenvalues, eigenvectors, and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices, as well as structured Schur forms and several orthogonal symplectic factorizations of such matrices. Many of the subroutines are already integrated in SLICOT and the library itself is not longer developed.
- Source code of HAPACK Version 1.1.1
- MATLAB scripts and MEX gateways
- The Square-Reduced Method for the Hamiltonian Eigenavalue Problem (TOMS 800)
Benchmark Collection for the Riccati Equation
The FORTRAN 77 and MATLAB subroutine sets CAREX and DAREX generate a bunch of benchmark problems with focus on the continuous time algebraic Riccati equation (CARE) or respectively to the discrete time algebraic Riccati equation (DARE). Details about the generated model problems and their usage are described in the publications listed below.