A modified Newton iteration for finding nonnegative Z-eigenpairs of a nonnegative tensor

Chun Hua Guo*, Wen-Wei Lin, Ching Sung Liu

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We propose a modified Newton iteration for finding some nonnegative Z-eigenpairs of a nonnegative tensor. When the tensor is irreducible, all nonnegative eigenpairs are known to be positive. We prove local quadratic convergence of the new iteration to any positive eigenpair of a nonnegative tensor, under the usual assumption guaranteeing the local quadratic convergence of the original Newton iteration. A big advantage of the modified Newton iteration is that it seems capable of finding a nonnegative eigenpair starting with any positive unit vector. Special attention is paid to transition probability tensors.

Original languageEnglish
Pages (from-to)595-616
Number of pages22
JournalNumerical Algorithms
Volume80
Issue number2
DOIs
StatePublished - 6 Feb 2019

Keywords

  • Modified Newton iteration
  • Nonnegative tensor
  • Nonnegative Z-eigenpair
  • Quadratic convergence
  • Transition probability tensor

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