In this paper, we mainly develop the well-known vector and matrix polynomial extrapolation methods in tensor framework. To this end, some new products between tensors are defined and the concept of positive definitiveness is extended for tensors corresponding to T-product. Furthermore, we discuss on the solution of least-squares problem associated with a tensor equation using Tensor Singular Value Decomposition (TSVD). Motivated by the effectiveness of some proposed vector extrapolation methods in earlier papers, we describe how an extrapolation technique can be also implemented on the sequence of tensors produced by truncated TSVD (TTSVD) for solving possibly ill-posed tensor equations.

在本文中，我们主要开发张量框架中众所周知的矢量和矩阵多项式外推方法。为此，定义了张量之间的一些新乘积，并将正定性的概念扩展到与T乘积相对应的张量。此外，我们讨论了使用张量奇异值分解（TSVD）解决与张量方程有关的最小二乘问题。出于较早论文中某些拟议的向量外推方法的有效性的推动，我们描述了如何在截断TSVD（TTSVD）产生的张量序列上实施外推技术，以解决可能存在的不适定张量方程。