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A symmetric structure-preserving QR algorithm for linear response eigenvalue problems

Tiexiang Li Ren-Cang Li Wen-Wei Lin

Numerical Linear Algebra mathscidoc:1912.43737

Linear Algebra and its Applications, 520, 191-214, 2017.5
In this paper, we present an efficient QR algorithm for solving the linear response eigenvalue problem H x= x, where H is -symmetric with respect to 0= diag (I n, I n). Based on newly introduced -orthogonal transformations, the QR algorithm preserves the -symmetric structure of H throughout the whole process, and thus guarantees the computed eigenvalues to appear pairwise (, ) as they should. With the help of a newly established implicit -orthogonality theorem, we incorporate the implicit multi-shift technique to accelerate the convergence of the QR algorithm. Numerical experiments are given to show the effectiveness of the algorithm.
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@inproceedings{tiexiang2017a,
  title={A symmetric structure-preserving QR algorithm for linear response eigenvalue problems},
  author={Tiexiang Li, Ren-Cang Li, and Wen-Wei Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205415683520301},
  booktitle={Linear Algebra and its Applications},
  volume={520},
  pages={191-214},
  year={2017},
}
Tiexiang Li, Ren-Cang Li, and Wen-Wei Lin. A symmetric structure-preserving QR algorithm for linear response eigenvalue problems. 2017. Vol. 520. In Linear Algebra and its Applications. pp.191-214. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205415683520301.
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