论文标题
应用应用的张量外推法
Tensor extrapolation methods with applications
论文作者
论文摘要
在本文中，我们主要开发了张量框架中众所周知的载体和基质多项式外推法。为此，定义了张量之间的一些新产品，并扩展了与T产品相对应的张量。此外，我们讨论了使用张量奇异值分解（TSVD）与张量方程相关的最小二乘问题的解决方案。由提出的向量外推法的有效性[Numer。算法，51（2009），195--208]，我们描述了如何在截短的TSVD（TTSVD）产生的张量序列上实施外推技术，以求解可能不足的张量张量的方程。
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 proposed vector extrapolation method in [Numer. Algorithms, 51 (2009), 195--208], 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.
