Iterative algorithms for computing US- and U-eigenpairs of complex tensors

Maolin Che, Liqun Qi, Yimin Wei

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)

Abstract

� 2016 Elsevier B.V. This paper is devoted to the computation of US-eigenpairs of complex symmetric tensors and U-eigenpairs of complex tensors. Based on the Takagi factorization of complex symmetric matrices, we derive an iterative algorithm for computing US-eigenpairs of complex symmetric tensors, denoted as QRCST Algorithm. We also observe that multiple US-eigenpairs can be found from a local permutation heuristic, which is effectively a tensor similarity transformation, resulting in the permuted version of QRCST. We then generalize our techniques to general complex tensors. Finally, we derive a higher order power type method for computing a US- or a U-eigenpair, similar to the higher-order power method for computing Z-eigenpairs of real symmetric tensors or a best rank-one approximation of real tensors. We illustrate our algorithms via numerical examples.
Original languageEnglish
Pages (from-to)547-564
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume317
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • Complex symmetric matrices
  • Complex symmetric tensors
  • Complex tensors
  • Takagi factorization
  • U-eigenpairs
  • US-eigenpairs

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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