A fast algorithm for the spectral radii of weakly reducible nonnegative tensors

Guanglu Zhou, Gang Wang, Liqun Qi, Mohammed Alqahtani

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)

Abstract

In this paper, we propose a fast algorithm for computing the spectral radii of symmetric nonnegative tensors. In particular, by this proposed algorithm, we are able to obtain the spectral radii of weakly reducible symmetric nonnegative tensors without requiring the partition of the tensors. As we know, it is very costly to determine the partition for large-sized weakly reducible tensors. Numerical results are reported to show that the proposed algorithm is efficient and also able to compute the spectral radii of large-sized tensors. As an application, we present an algorithm for testing the positive definiteness of Z-tensors. By this algorithm, it is guaranteed to determine the positive definiteness for any Z-tensor.
Original languageEnglish
Article numbere2134
JournalNumerical Linear Algebra with Applications
Volume25
Issue number2
DOIs
Publication statusPublished - 1 Mar 2018

Keywords

  • positive definiteness
  • spectral radius
  • symmetric nonnegative tensors
  • Z-tensors

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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