Quaternion matrix decomposition and its theoretical implications

被引：1
|
作者：
He, Chang [1 ]
Jiang, Bo [2 ]
Zhu, Xihua [3 ]
机构：
[1] Shanghai Univ Finance & Econ, Res Inst Interdisciplinary Sci, Shanghai 200433, Peoples R China
[2] Shanghai Univ Finance & Econ, Sch Informat Management & Engn, Res Inst Interdisciplinary Sci, Shanghai 200433, Peoples R China
[3] Shanghai Business Sch, Fac Business Informat, Shanghai 200235, Peoples R China
来源：
JOURNAL OF GLOBAL OPTIMIZATION | 2023年 / 87卷 / 2-4期
关键词：
Matrix rank-one decomposition; Quaternion; Joint numerical range; S-Procedure; Quadratic optimization; STRUCTURE-PRESERVING METHOD; CONVEX-OPTIMIZATION;
D O I：
10.1007/s10898-022-01210-7
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in Ai W et al (Math Progr 128(1):253-283, 2011), Huang Y, Zhang S (Math Oper Res 32(3):758-768, 2007), Sturm JF, Zhang S (Math Oper Res 28(2):246-267 2003). The enhanced property can be used to drive some improved results in joint numerical range, S-Procedure and quadratically constrained quadratic programming (QCQP) in the quaternion domain, demonstrating the capability of our new decomposition technique.
引用
收藏
页码：741 / 758
页数：18
相关论文
共 50 条
  • [1] Quaternion matrix decomposition and its theoretical implications
    Chang He
    Bo Jiang
    Xihua Zhu
    [J]. Journal of Global Optimization, 2023, 87 : 741 - 758
  • [2] RANDOMIZED QUATERNION MATRIX UTV DECOMPOSITION AND ITS APPLICATIONS IN QUATERNION MATRIX OPTIMIZATION
    Xu, Renjie
    Wei, Yimin
    [J]. PACIFIC JOURNAL OF OPTIMIZATION, 2024, 20 (02): : 185 - 211
  • [3] Incremental quaternion singular value decomposition and its application for low rank quaternion matrix completion
    Xu, Yang
    Gao, Kaixin
    [J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (06):
  • [4] Quaternion matrix singular value decomposition and its applications for color image processing
    Pei, SC
    Chang, JH
    Ding, JJ
    [J]. 2003 INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOL 1, PROCEEDINGS, 2003, : 805 - 808
  • [5] Jacobi method for quaternion matrix singular value decomposition
    Le Bihan, Nicolas
    Sangwine, Stephen J.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (02) : 1265 - 1271
  • [6] QR decomposition of dual quaternion matrix and blind watermarking scheme
    Zhang, Mingcui
    Li, Ying
    Wang, Tao
    Sun, Jianhua
    [J]. NUMERICAL ALGORITHMS, 2024,
  • [7] A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications
    Zhang, Dong
    Jiang, Tongsong
    Jiang, Chuan
    Wang, Gang
    [J]. NUMERICAL ALGORITHMS, 2024, 95 (01) : 267 - 283
  • [8] A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications
    Dong Zhang
    Tongsong Jiang
    Chuan Jiang
    Gang Wang
    [J]. Numerical Algorithms, 2024, 95 : 267 - 283
  • [9] On a Solution of the Quaternion Matrix Equation and Its Applications
    Jiang, Tongsong
    Ling, Sitao
    [J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2013, 23 (03) : 689 - 699
  • [10] Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm
    Wang, Tao
    Li, Ying
    Wei, Musheng
    Xi, Yimeng
    Zhang, Mingcui
    [J]. NUMERICAL ALGORITHMS, 2024,
12345