The tensor splitting methods for solving tensor absolute value equation


Recently, D.-D. Liu et al. (2018) presented the tensor splitting methods for solving multilinear systems and S.-Q. Du et al. (2018) generalized tensor absolute value equations. In this paper, we verify the existence of solutions of tensor absolute value equations and propose the tensor splitting methods for solving this class of equation. Furthermore, the convergence analysis of the tensor splitting method is also studied under suitable conditions. Finally, numerical examples show that our algorithm is an efficient iterative method.

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Correspondence to Chang-Feng Ma.

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Communicated by Jinyun Yuan.

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Bu, F., Ma, C. The tensor splitting methods for solving tensor absolute value equation. Comp. Appl. Math. 39, 178 (2020).

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  • Tensor absolute value equation
  • Tensor splitting
  • Strong \(\mathcal {M}\)-tensor

Mathematics Subject Classification

  • 15A69
  • 15A72
  • 53A45