A new method based on the semi-tensor product of matrices for solving communicative quaternion matrix equation ∑i=1kAiXBi=C and its application

IF 1.3 3区 数学 Q2 MATHEMATICS, APPLIED
Mingcui Zhang, Ying Li, Jianhua Sun, Xueling Fan, Anli Wei
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引用次数: 0

Abstract

This paper studies the least squares problem of the commutative quaternion matrix equation (1.1), finds its minimal norm least squares (anti-)Hermitian solution. In the process of completing this work, we generalize the semi-tensor product of real matrices to the commutative quaternion matrices, then use it to extend the vector operators to the commutative quaternion matrix and propose the L-representation, which transforms the intricate commutative quaternion matrix equation into a solvable system of real linear equations, we also use GH-representation to reduce the complexity of the operation and greatly save the operation time. This can be illustrated by numerical examples in the paper. In addition, we take a special kind of commutative quaternion: reduced biquaternion as an example, and compare our method with another method in reference [33] to prove the effectiveness of our method. Finally, we apply the method used in this paper to symmetric color image restoration.
基于矩阵半张量积求解交流四元数矩阵方程∑i=1kAiXBi=C的新方法及其应用
研究了可交换四元数矩阵方程(1.1)的最小二乘问题,得到了其最小范数最小二乘(反)厄米特解。在完成这项工作的过程中,我们将实数矩阵的半张量积推广到可交换四元数矩阵,然后利用它将向量算子推广到可交换四元数矩阵,并提出l表示,将复杂的可交换四元数矩阵方程转化为可解的实数线性方程组,同时采用gh表示,降低了运算的复杂性,大大节省了运算时间。本文通过数值算例说明了这一点。此外,我们还以一种特殊的交换四元数:约简四元数为例,将我们的方法与文献[33]中的另一种方法进行了比较,证明了我们方法的有效性。最后,将本文方法应用于对称彩色图像的复原。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.90
自引率
7.70%
发文量
71
审稿时长
6-12 weeks
期刊介绍: Founded in 1870, by Gaston Darboux, the Bulletin publishes original articles covering all branches of pure mathematics.
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