论文标题
通过$ t $ - 产品计算张量的广义逆了
Computation of Generalized Inverses of Tensors via $t$-Product
论文作者
论文摘要
张量的广义逆，在计算数学和数值分析中起着越来越重要的作用。在环的代数结构内开发张量的广义对逆的理论是适当的。在本文中，我们研究了在交换环和非交换环上的张量的不同广义逆。提供了几个数值示例以支持理论结果。我们还提出了用于计算内部倒置，摩尔 - 芬罗逆和加权的摩尔 - 碳纤维逆量的算法，在非交通环上的张量。通过应用这些想法来解决图像造影问题，证明了一些结果的能力。
Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In this paper, we study different generalized inverses of tensors over a commutative ring and a non-commutative ring. Several numerical examples are provided in support of the theoretical results. We also propose algorithms for computing the inner inverses, the Moore-Penrose inverse, and weighted Moore-Penrose inverse of tensors over a non-commutative ring. The prowess of some of the results is demonstrated by applying these ideas to solve an image deblurring problem.
