Continuation methods for computing Z-/H-eigenpairs of nonnegative tensors

Yueh Cheng Kuo, Wen-Wei Lin, Ching Sung Liu*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)71-88
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume340
DOIs
StatePublished - 1 Oct 2018

Keywords

  • Continuation method
  • H-eigenpair
  • Nonnegative tensor
  • Tensor eigenvalue problem
  • Z-eigenpair

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