Solving reduced biquaternion matrices equation Σi=1k AiXBi = C with special structure based on semi-tensor product of matrices

被引：5

作者：

Ding, Wenxv ^{[1
,2
]}

Li, Ying ^{[1
,2
]}

Wei, Anli ^{[1
,2
]}

Liu, Zhihong ^{[1
,2
]}

机构：

[1] Liaocheng Univ, Coll Math Sci, Liaocheng 252000, Shandong, Peoples R China

[2] Res Ctr Semitensor Prod Matrices Theory & Applica, Liaocheng 252000, Shandong, Peoples R China

来源：

AIMS MATHEMATICS | 2021年 / 7卷 / 03期

基金：

中国国家自然科学基金;

关键词：

semi-tensor product of matrices; reduced biquaternion; matrix equation; real vector representation;

D O I：

10.3934/math.2022181

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of reduced biquaternion matrix equation (1.1). Several numerical examples show that the proposed algorithm is feasible at last.

引用

页码：3258 / 3276

页数：19

共 16 条

[1] Generalised semi-tensor product of matrices
Cheng, Daizhan
Liu, Zequn
Xu, Zhenhui
Shen, Tielong
[J]. IET CONTROL THEORY AND APPLICATIONS, 2020, 14 (01) : 85 - 95
[2] From STP to game-based control
Cheng, Daizhan
Qi, Hongsheng
Liu, Zequn
[J]. SCIENCE CHINA-INFORMATION SCIENCES, 2018, 61 (01)
[3] Cheng DH, 2011, COMMUN CONTROL ENG, P1, DOI 10.1007/978-0-85729-097-7
[4] Golub GH, 2012, MATRIX COMPUTATIONS
[5] Isokawa T, 2010, IEEE IJCNN
[6] Least-squares solutions of the reduced biquaternion matrix equation AX=B and their applications in colour image restoration
Kosal, Hidayet Huda
[J]. JOURNAL OF MODERN OPTICS, 2019, 66 (18) : 1802 - 1810
[7] Kyrchei I. I., 2019, Abstr. Appl. Anal., V2019, DOI [10.1155/2019/5926832, DOI 10.1155/2019/5926832]
[8] Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
Kyrchei, Ivan I.
[J]. JOURNAL OF MATHEMATICS, 2018, 2018
[9] Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems
Lu, Jianquan
Li, Haitao
Liu, Yang
Li, Fangfei
[J]. IET CONTROL THEORY AND APPLICATIONS, 2017, 11 (13) : 2040 - 2047
[10] Commutative reduced biquaternions and their Fourier transform for signal and image processing applications
Pei, SC
Chang, JH
Ding, JJ
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2004, 52 (07) : 2012 - 2031

← 1 2 →