A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems

Tiexiang Li Eric King-wah Chu Wen-Wei Lin

Numerical Analysis and Scientific Computing mathscidoc:1912.43745

Journal of computational and applied mathematics, 233, (8), 1733-1745, 2010.2
We propose a structure-preserving doubling algorithm for a quadratic eigenvalue problem arising from the stability analysis of time-delay systems. We are particularly interested in the eigenvalues on the unit circle, which are difficult to estimate. The convergence and backward error of the algorithm are analyzed and three numerical examples are presented. Our experience shows that our algorithm is efficient in comparison to the few existing approaches for small to medium size problems.
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@inproceedings{tiexiang2010a,
  title={A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems},
  author={Tiexiang Li, Eric King-wah Chu, and Wen-Wei Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205445291385309},
  booktitle={Journal of computational and applied mathematics},
  volume={233},
  number={8},
  pages={1733-1745},
  year={2010},
}
Tiexiang Li, Eric King-wah Chu, and Wen-Wei Lin. A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems. 2010. Vol. 233. In Journal of computational and applied mathematics. pp.1733-1745. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205445291385309.
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