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.

中文翻译：

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张量绝对值方程的张量分裂方法

最近，D.-D。刘等。（2018）提出了用于解决多线性系统和S.-Q的张量分裂方法。杜等。（2018）广义张量绝对值方程。在本文中，我们验证了张量绝对值方程解的存在性，并提出了用于解决此类方程的张量分裂方法。此外，还研究了张量分裂方法在合适条件下的收敛性分析。最后，数值算例表明我们的算法是一种有效的迭代方法。