Related References

[Ben00]

P. Benner. Symplectic balancing of Hamiltonian matrices. SIAM J. Sci. Comput., 22(5):1885-1904, 2000.

[BK04]

P. Benner and D. Kressner. Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II. 2004. accepted for publication in ACM Transactions on Mathematical Software, September 2005. (Gzipped PostScript, 25 pages, 260615 bytes) (PDF, 251737 bytes)

[BK05]

P. Benner and D. Kressner. New Hamiltonian eigensolvers with applications in control. March 2005, to appear in Proceedings of 44th IEEE Conference on Decision and European Control Conference ECC 2005, 2005. (Gzipped PostScript, 6 pages, 104588 bytes) (PDF, 118535 bytes)

[BKM05]

P. Benner, D. Kressner, and V. Mehrmann. Skew-Hamiltonian and Hamiltonian eigenvalue problems: Theory, algorithms and applications. In Z. Drmac, M. Marusic, and Z. Tutek, editors, Proceedings of the Conference on Applied Mathematics and Scientific Computing, Brijuni (Croatia), June 23-27, 2003, pages 3-39. Springer-Verlag, 2005. (Gzipped PostScript, 41 pages, 283580 bytes) (PDF, 364340 bytes)

[BMX97]

P. Benner, V. Mehrmann, and H. Xu. A new method for computing the stable invariant subspace of a real Hamiltonian matrix. J. Comput. Appl. Math., 86:17-43, 1997.

[BMX98]

P. Benner, V. Mehrmann, and H. Xu. A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils. Numerische Mathematik, 78(3):329-358, 1998.

[BMX99]

P. Benner, V. Mehrmann, and H. Xu. A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems. Electron. Trans. Numer. Anal., 8:115-126, 1999.

[Kre01]

D. Kressner. An efficient and reliable implementation of the periodic QZ algorithm. In IFAC Workshop on Periodic Control Systems, 2001. (Gzipped PostScript, 6 pages, 91883 bytes)

[Kre03a]

D. Kressner. Block algorithms for orthogonal symplectic factorizations. BIT Numerical Mathematics, 43(4):775-790, 2003. (Gzipped PostScript, 16 pages, 202638 bytes)

[Kre03b]

D. Kressner. Perturbation bounds for isotropic invariant subspaces of skew-Hamiltonian matrices. 2003. To appear in SIAM J. Matrix Anal. Appl. (Gzipped PostScript, 15 pages, 205373 bytes)

[PVL81]

C. Paige and C. Van Loan. A Schur decomposition for Hamiltonian matrices. Linear Algebra Appl., 41:11-32, 1981.

[Van84]

C. F. Van Loan. A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix. Linear Algebra Appl., 61:233-251, 1984.