| 报告题目： | computing hamiltonian schur form of hamiltonian matrices |
| 报 告 人： | prof delin chu |
| department of mathematics, national university of singapore | |
| 报告时间： | 12月27日下午3:30pm开始 |
| 报告地点： | 九龙湖数学系第一报告厅 |
| 相关介绍： | let m be a 2n-by-2n hamiltonian matrix with no eigenvalues on the imaginary axis. then there is an orthogonal-symplectic similarity transformation of m to hamiltonian schur form, revealing the spectrum and stable invariant subspace of m. this was proved by c. c. paige and c.van loan in a paper published in 1981. the proof given in that paper was nonconstructive. ever since, the problem of developing a structure-preserving and backward-stable algorithm with complexity o(n^3) to compute the hamiltonian schur form of a 2n-by-2n hamiltonian matrix proved difficult to solve however, so much so that it came to be known as van loans curse. in this talk we will introduce a new method that may meet these criteria for computing the hamiltonian schur form of a 2n-by-2n hamiltonian matrix m without purely imaginary eigenvalues. the new method is structure-preserving and is of complexity o(n^3). it is implemented using orthogonal-symplectic transformations only and many numerical results demonstrate that it performs well and is backward stable in cases where there are no eigenvalues too close to the imaginary axis. |
