The palindromic generalized eigenvalue problem A x= Ax: Numerical solution and applications

Tiexiang Li Chun-Yueh Chiang Eric King-wah Chu Wen-Wei Lin

Numerical Linear Algebra mathscidoc:1912.43736

Linear Algebra and its Applications, 434, (11), 2269-2284, 2011.6
In this paper, we propose the palindromic doubling algorithm (PDA) for the palindromic generalized eigenvalue problem (PGEP) A x= Ax. We establish a complete convergence theory of the PDA for PGEPs without unimodular eigenvalues, or with unimodular eigenvalues of partial multiplicities two (one or two for eigenvalue 1). Some important applications from the vibration analysis and the optimal control for singular descriptor linear systems will be presented to illustrate the feasibility and efficiency of the PDA.
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@inproceedings{tiexiang2011the,
  title={The palindromic generalized eigenvalue problem A x= Ax: Numerical solution and applications},
  author={Tiexiang Li, Chun-Yueh Chiang, Eric King-wah Chu, and Wen-Wei Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205412429885300},
  booktitle={Linear Algebra and its Applications},
  volume={434},
  number={11},
  pages={2269-2284},
  year={2011},
}
Tiexiang Li, Chun-Yueh Chiang, Eric King-wah Chu, and Wen-Wei Lin. The palindromic generalized eigenvalue problem A x= Ax: Numerical solution and applications. 2011. Vol. 434. In Linear Algebra and its Applications. pp.2269-2284. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205412429885300.
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