Computing Hamiltonian Schur Form of Hamiltonian Matrices Arising from Algebraic Riccati Equations
主 题: Computing Hamiltonian Schur Form of Hamiltonian Matrices Arising from Algebraic Riccati Equations
报告人: 储德林教授（新加坡国立大学数学系）
时 间: 2013-06-12 10:00-11:00
地 点: 理科一号楼1418
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 Loan\'s 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 on algebraic Riccati equations
demonstrate that it performs
