Solving Multi-linear Systems with M -Tensors

Weiyang DING, Yimin Wei*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

163 Citations (Scopus)


This paper is concerned with solving some structured multi-linear systems, especially focusing on the equations whose coefficient tensors are M-tensors, or called M-equations for short. We prove that a nonsingular M-equation with a positive right-hand side always has a unique positive solution. Several iterative algorithms are proposed for solving multi-linear nonsingular M-equations, generalizing the classical iterative methods and the Newton method for linear systems. Furthermore, we apply the M-equations to some nonlinear differential equations and the inverse iteration for spectral radii of nonnegative tensors.

Original languageEnglish
Pages (from-to)689-715
Number of pages27
JournalJournal of Scientific Computing
Issue number2
Publication statusPublished - 1 Aug 2016

Scopus Subject Areas

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

User-Defined Keywords

  • Gauss–Seidel method
  • Inverse iteration
  • Jacobi method
  • M-tensor
  • Multi-linear system
  • Newton method
  • Nonnegative solution
  • Nonnegative tensor
  • Triangular system


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