Strictly nonnegative tensors and nonnegative tensor partition

ShengLong L. Hu, ZhengHai H. Huang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

52 Citations (Scopus)

Abstract

We introduce a new class of nonnegative tensors-strictly nonnegative tensors. A weakly irreducible nonnegative tensor is a strictly nonnegative tensor but not vice versa. We show that the spectral radius of a strictly nonnegative tensor is always positive. We give some necessary and sufficient conditions for the six well-conditional classes of nonnegative tensors, introduced in the literature, and a full relationship picture about strictly nonnegative tensors with these six classes of nonnegative tensors. We then establish global R-linear convergence of a power method for finding the spectral radius of a nonnegative tensor under the condition of weak irreducibility. We show that for a nonnegative tensor T, there always exists a partition of the index set such that every tensor induced by the partition is weakly irreducible; and the spectral radius of T can be obtained from those spectral radii of the induced tensors. In this way, we develop a convergent algorithm for finding the spectral radius of a general nonnegative tensor without any additional assumption. Some preliminary numerical results show the feasibility and effectiveness of the algorithm.
Original languageEnglish
Pages (from-to)181-195
Number of pages15
JournalScience China Mathematics
Volume57
Issue number1
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • nonnegative tensor
  • spectral radius
  • strict nonnegativity
  • weak irreducibility

ASJC Scopus subject areas

  • Mathematics(all)

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