ncku-talk2007-04-23

NCKU Math colloquium

DATE 2007-04-23　16:10-17:00

PLACE 數學館地下室演講廳

SPEAKER 錢江(Jiang Qian)（清華大學數學系博士後）

TITLE Structure preserving methods for palindromic quadratic eigenvalue problems

ABSTRACT We consider the palindromic quadratic eigenvalues problem $(\lambda^2 A_1^\top+\lambda A_0+A_1)x=0$ with $A_1,A_0\in \mathbb{C} ^ {n\times n}$ and $A_0^\top =A_0$, which arises in the vibration analysis of fast trains and rail tracks. The eigenvalues of such palindromic QEP have symplectic structure, which means that they appear in pair $(\lambda,1/\lambda)$.
We propose two methods for finding all the eigenvalues and eigenvectors of the palindromic QEP, which preserve the special symplectic structure, and use unitary transformations whenever possible, and hence are numerically reliable. Numerical examples illustrate the good behavior of the methods.

NCKU Math colloquium

DATE	2007-04-23　16:10-17:00

PLACE	數學館地下室演講廳

SPEAKER	錢江(Jiang Qian)（清華大學數學系博士後）

TITLE	Structure preserving methods for palindromic quadratic eigenvalue problems

ABSTRACT	We consider the palindromic quadratic eigenvalues problem $(\lambda^2 A_1^\top+\lambda A_0+A_1)x=0$ with $A_1,A_0\in \mathbb{C} ^ {n\times n}$ and $A_0^\top =A_0$, which arises in the vibration analysis of fast trains and rail tracks. The eigenvalues of such palindromic QEP have symplectic structure, which means that they appear in pair $(\lambda,1/\lambda)$. We propose two methods for finding all the eigenvalues and eigenvectors of the palindromic QEP, which preserve the special symplectic structure, and use unitary transformations whenever possible, and hence are numerically reliable. Numerical examples illustrate the good behavior of the methods.