A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M -tensors

Hongjin He, Chen Ling, Liqun Qi, Guanglu Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

29 Citations (Scopus)


We consider multilinear systems of equations whose coefficient tensors are M-tensors. Multilinear systems of equations have many applications in engineering and scientific computing, such as data mining and numerical partial differential equations. In this paper, we show that solving multilinear systems with M-tensors is equivalent to solving nonlinear systems of equations where the involving functions are P-functions. Based on this result, we propose a Newton-type method to solve multilinear systems with M-tensors. For a multilinear system with a nonsingular M-tensor and a positive right side vector, we prove that the sequence generated by the proposed method converges to the unique solution of the multilinear system and the convergence rate is quadratic. Numerical results are reported to show that the proposed method is promising.

Original languageEnglish
Pages (from-to)1718-1741
Number of pages24
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - 1 Sep 2018


  • M-tensor
  • Multilinear systems
  • Newton’s method
  • quadratic convergence

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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