Solving a Structured Quadratic Eigenvalue Problem by a Structure-Preserving Doubling Algorithm

@article{Guo2010SolvingAS,
  title={Solving a Structured Quadratic Eigenvalue Problem by a Structure-Preserving Doubling Algorithm},
  author={Chun-Hua Guo and Wen-Wei Lin},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2010},
  volume={31},
  pages={2784-2801}
}
In studying the vibration of fast trains, we encounter a palindromic quadratic eigenvalue problem (QEP) $(\lambda^{2}A^{T}+\lambda Q+A)z=0$, where $A,Q\in\mathbb{C}^{n\times n}$ and $Q^{T}=Q$. Moreover, the matrix $Q$ is block tridiagonal and block Toeplitz, and the matrix $A$ has only one nonzero block in the upper-right corner. So most of the eigenvalues of the QEP are zero or infinity. In a linearization approach, one typically starts with deflating these known eigenvalues for the sake of… 

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