Return to Colloquia & Seminar listing
A Numerically Stable Structure Preserving Method for the Eigenvalue problem of Hamiltonian Matrices and the Solutions of Algebraic Riccati Equations.
Special Events| Speaker: | Dr. Hongguo Xu, TU-Chemnitz |
| Location: | 1065 EU II |
| Start time: | Wed, Jun 2 1999, 10:00AM |
Description
The eigenvalue problem of the Hamiltonian matrices has many applications in
practice. The major application to the linear control system and information
theory is the solutions of the algebraic Riccati equations. The main challenge
of this problem in numerical computation aspect is how to use the algebraic
structures of the matrices. In this talk we first show a new backward stable
structure preserving numerical algorithm for computing the eigenvalues of
the Hamiltonian matrices. The main trick is to compute a symplectic URV like
decomposition of a Hamiltonian matrix $cH$. Using this decomposition and the
relation between $cH$ and the extended matrix $mat{cc}0&cH\cH&0
ix$,
we then develop a numerical method to compute the Lagrangian invariant subspace as well as the solutions of the associated algebraic Riccati equation.
The similar method for the complex Hamiltonian matrices is also given.