Structure preservation: a challenge in computational control
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
On the computation of few eigenvalues of positive definite Hamiltonian matrices
Future Generation Computer Systems
Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II
ACM Transactions on Mathematical Software (TOMS)
On the computation of few eigenvalues of positive definite Hamiltonian matrices
Future Generation Computer Systems
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
A new structure-preserving method for quaternion Hermitian eigenvalue problems
Journal of Computational and Applied Mathematics
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We discuss the balancing of Hamiltonian matrices by structure preserving similarity transformations. The method is closely related to balancing nonsymmetric matrices for eigenvalue computations as proposed by Osborne [J. ACM, 7 (1960), pp. 338--345]and Parlett and Reinsch [Numer. Math., 13 (1969), pp. 296--304] and implemented in most linear algebra software packages. It is shown that isolated eigenvalues can be deflated using similarity transformations with symplectic permutation matrices. Balancing is then based on equilibrating row and column norms of the Hamiltonian matrix using symplectic scaling matrices. Due to the given structure, it is sufficient to deal with the leading half rows and columns of the matrix. Numerical examples show that the method improves eigenvalue calculations of Hamiltonian matrices as well as numerical methods for solving continuous-time algebraic Riccati equations.