A practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor

Yiju Wang, Liqun Qi, Xinzhen Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

81 Citations (Scopus)


In this paper, we consider a bi-quadratic homogeneous polynomial optimization problem over two unit spheres arising in nonlinear elastic material analysis and in entanglement studies in quantum physics. The problem is equivalent to computing the largest M-eigenvalue of a fourth-order tensor. To solve the problem, we propose a practical method whose validity is guaranteed theoretically. To make the sequence generated by the method converge to a good solution of the problem, we also develop an initialization scheme. The given numerical experiments show the effectiveness of the proposed method.
Original languageEnglish
Pages (from-to)589-601
Number of pages13
JournalNumerical Linear Algebra with Applications
Issue number7
Publication statusPublished - 1 Jul 2009


  • Initialization scheme
  • M-eigenvalue
  • Power method

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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