The notation of Moore-Penrose inverse of matrices has been extended from matrix space to even-order tensor space with Einstein product. In this paper, we give the numerical study on the Moore-Penrose inverse of tensors via the Einstein product. More precisely, we transform the calculation of Moore-Penrose inverse of tensors via the Einstein product into solving a class of tensor equations via the Einstein product. Then, by means of the conjugate gradient method, we obtain the approximate Moore-Penrose inverse of tensors via the Einstein product. Finally, we report some numerical examples to show the efficiency of the proposed methods and testify the conclusion suggested in this paper.

矩阵的Moore-Penrose逆的表示法已经用爱因斯坦积从矩阵空间扩展到偶数张量空间。在本文中，我们通过爱因斯坦乘积对张量的Moore-Penrose逆进行了数值研究。更确切地说，我们将通过爱因斯坦积的张量的摩尔-彭罗斯逆变换的计算转换为通过爱因斯坦积求解一类张量方程。然后，通过共轭梯度法，我们通过爱因斯坦积获得张量的近似Moore-Penrose逆。最后，我们报告了一些数值算例，以证明所提方法的有效性，并证明本文提出的结论。