报告人: 卢琳璋教授（厦门大学数学科学学院二级教授）

报告标题: A structure-exploiting algorithm for solving a palindromic quadratic eigenvalue problem

时间: 2015-6-15（星期一）下午4：30

报告地点：数学系实验室

摘要：

In this talk, we discuss how to solve numerically  the palindromic quadratic eigenvalue problem (PQEP) (λ² A^T+ λ Q + A)z=0 arising from the vibration analysis of high speed trains,  where A, Q m-by-m are matrices with special structures: both Q and A are m-by-m block matrices with each block being q-by-q, and moreover they are complex symmetric, block tridiagonal, and block Toeplitz. Recently, Guo and Lin (SIAM J. Matrix Anal. Appl., 31 (2010), 2784--2801) proposed an efficient solvent approach to solve this PQEP by computing the so-called stabilizing solution to the n-by-n matrix equation X+A^TX^-1A=Q via the doubling algorithm. It is shown here that the stabilizing solution X differs from Q only in its (m,m)th block position, and thus it suffices to only compute that block. The latter is shown to satisfy another matrix equation having the same form as X+A^TX^-1A=Q but of q-by-q. We then apply the doubling algorithm to the q-by-q matrix equation to the block and the whole stabilizing solution.
    Numerical examples are presented to show the effectiveness of the new method.

 

汕头大学理学院

2015年6月12日