Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) $ℳ$‐tensors. In this article, we introduce H‐splitting and H‐compatible splitting and investigate the relationship between these different splittings and their convergence. Meanwhile, we also consider a preconditioned AOR iterative method for solving tensor equations with nonsingular $\mathscr{H}$‐tensors. We prove its convergence and give a comparison result on the spectral radius of the iteration tensor for the case when $𝒜$ is a nonsingular $ℳ$‐tensor. Numerical examples are also given to illustrate our methods.

中文翻译：

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tens张量方程的预处理张量分裂AOR迭代方法

基于张量的弱正则分裂，预处理技术在求解具有非奇异（强）的张量方程时显示出了很大的优势 $ℳ$张量。在本文中，我们介绍了H分裂和H兼容分裂，并研究了这些不同分裂及其收敛之间的关系。同时，我们还考虑了一种求解非奇异张量方程的预处理AOR迭代方法$\mathscr{H}$张量。我们证明了它的收敛性，并给出了在以下情况下迭代张量的谱半径的比较结果：$𝒜$ 是非单数 $ℳ$张量。数值例子也说明了我们的方法。