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The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-06-11 , DOI: 10.1080/03081087.2020.1779172
Qing-Wen Wang 1 , Ru-Yuan Lv 1 , Yang Zhang 2
Affiliation  

In this paper, we investigate the least-squares solution with the least norm to the following system of tensor equations over quaternions A1NX=D1,YNB2=D2,A3NXNB3=D3,A4NYNB4=D4,A5NX+YNB5=D5, where X,Y are unknown quaternion tensors and the others are given quaternion tensors. Using the expressions of the Moore-Penrose inverses of partitioned tensors, we give a representation of the solution and an algorithm to compute this solution.



中文翻译:

四元数代数上张量方程组的最小范数的最小二乘解

在本文中,我们研究了以下四元数张量方程组的最小范数的最小二乘解一个1*ñX=D1,*ñ2=D2,一个3*ñX*ñ3=D3,一个4*ñ*ñ4=D4,一个5*ñX+*ñ5=D5,在哪里X,是未知的四元数张量,其他的是四元数张量。使用分区张量的 Moore-Penrose 逆表达式,我们给出了解的表示和计算该解的算法。

更新日期:2020-06-11
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