In this article, we propose some subspace methods such as the conjugate residual, generalized conjugate residual, biconjugate gradient, conjugate gradient squared and biconjugate gradient stabilized methods based on the tensor forms for solving the tensor equation involving the Einstein product. These proposed algorithms keep the tensor structure. The convergence analysis shows that the proposed methods converge to the solution of the tensor equation for any initial value. Some numerical results confirm the feasibility and applicability of the proposed algorithms in practice.

中文翻译：

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求解涉及爱因斯坦积的张量方程的数值子空间算法

在本文中，我们基于张量形式提出了一些子空间方法，例如共轭残差，广义共轭残差，双共轭梯度，共轭梯度平方和双共轭梯度稳定方法，以求解涉及爱因斯坦积的张量方程。这些提出的算法保持张量结构。收敛性分析表明，对于任何初始值，所提出的方法都收敛于张量方程的解。一些数值结果证实了所提算法在实践中的可行性和适用性。