Continuation Methods for Computing Z-/H-eigenpairs of Nonnegative Tensors

Yueh-Cheng Kuo National University of Kaohsiung Wen-Wei Lin National Chiao Tung University Ching-Sung Liu National University of Kaohsiung

Numerical Analysis and Scientific Computing mathscidoc:1702.25081

In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.
continuation method, nonnegative tensor, Z-eigenpair, H-eigenpair, tensor eigenvalue problem
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@inproceedings{yueh-chengcontinuation,
  title={Continuation Methods for Computing  Z-/H-eigenpairs of Nonnegative Tensors},
  author={Yueh-Cheng Kuo, Wen-Wei Lin, and Ching-Sung Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170220105123911049477},
}
Yueh-Cheng Kuo, Wen-Wei Lin, and Ching-Sung Liu. Continuation Methods for Computing Z-/H-eigenpairs of Nonnegative Tensors. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170220105123911049477.
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