Linear convergence of the LZI algorithm for weakly positive tensors

Liping Zhang, Liqun Qi, Yi Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

28 Citations (Scopus)

Abstract

We define weakly positive tensors and study the relations among essentially positive tensors, weakly positive tensors, and primitive tensors. In particular, an explicit linear convergence rate of the Liu-Zhou-Ibrahim(LZI) algorithm for finding the largest eigenvalue of an irreducible nonnegative tensor, is established for weakly positive tensors. Numerical results are given to demonstrate linear convergence of the LZI algorithm for weakly positive tensors.
Original languageEnglish
Pages (from-to)24-33
Number of pages10
JournalJournal of Computational Mathematics
Volume30
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • Irreducible nonnegative tensor
  • Largest eigenvalue
  • Linear convergence
  • Weakly positive tensor

ASJC Scopus subject areas

  • Computational Mathematics

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