| 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. |
