Conservative perturbations of positive definite Hamiltonian matrices

Numerical Linear Algebra with Applications

Volumn 12, Issue 2-3, 2005, Pages 117-125

  Amodio, Pierluigi ^a   Iavernaro, F ^a   Trigiante, D ^b  

^a UNIVERSITY OF BARI   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Eigenvalues; Hamiltonian matrices; Perturbations

Indexed keywords

EID: 20744440809     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.409     Document Type: Article

References (12)

1. Lancaster P, Rodman L. The Algebraic Riccati Equation. Oxford University Press: Oxford, 1995.
2. Rosen I, Wang C. A multilevel technique for the approximate solution of operator Lyapunov and algebraic Riccati equations. SIAM Journal on Matrix Analysis and Applications 1992; 32:514-541.
3. Ammar G, Mehrmann V. On Hamiltonian and symplectic Hessenberg forms. Linear Algebra and Its Applications 1991; 149:55-72.
4. Lin W, Mehrmann V, Xu H. Canonical forms for Hamiltonian and symplectic matrices and pencils. Linear Algebra and Its Applications 1999; 302-303:469-533.
5. Benner P. Symplectic balancing of Hamiltonian matrices. SIAM Journal on Scientific Computing 2001; 22(5): 1885-1904.
6. Benner P, Faßbender H. An implicit restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem. Linear Algebra and Its Applications 1997; 263:75-111.
7. Bunse-Gerstner A. Matrix factorization for symplectic QR-like methods. Linear Algebra and Its Applications 1986; 83:49-77.
8. Byers R. A Hamiltonian QR-algorithm. SIAM Journal on Scientific and Statistical Computing 1986; 7: 212-229.
9. Van Loan C. A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix. Linear Algebra and its Applications 1984; 16:233-251.
10. Meyer KR, Hall GR. Introduction to Hamiltonian Dynamical Systems and the n-hody Problem. Springer: New York, 1992.
11. Amodio P, Iavernaro F, Trigiante D. Symmetric schemes and Hamiltonian perturbations of linear Hamiltonian problems. Numerical Linear Algebra with Applications 2005; 12.
12. Brugnano L, Trigiante D. Solving ODEs by Linear Multistep Initial and Boundary Value Methods. Gordon & Breach: Amsterdam, 1998.