Least-squares Hermitian problem of complex matrix equation (AXB, CXD) = (E, F)

被引：0
|
作者：
Wang, Peng [1 ,2 ]
Yuan, Shifang [1 ]
Xie, Xiangyun [1 ]
机构：
[1] Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Peoples R China
[2] Wuhan Univ Technol, Sch Comp Sci & Technol, Wuhan 430070, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2016年
关键词：
matrix equation; least-squares solution; Hermitian matrices; Moore-Penrose generalized inverse; MINIMUM-NORM;
D O I：
10.1186/s13660-016-1231-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a direct method to solve the least-squares Hermitian problem of the complex matrix equation (AXB, CXD) = (E, F) with complex arbitrary coefficient matrices A, B, C, D and the right-hand side E, F. This method determines the least-squares Hermitian solution with the minimum norm. It relies on a matrix-vector product and the Moore-Penrose generalized inverse. Numerical experiments are presented which demonstrate the efficiency of the proposed method.
引用
收藏
页数：13
相关论文
共 50 条
  • [11] Least Squares η - Hermitian Solution for Quaternion Matrix Equation AXB = C
    Yuan, Shifang
    INFORMATION COMPUTING AND APPLICATIONS, PT 1, 2012, 307 : 300 - 305
  • [12] Direct methods on η-Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F)
    Li, Ming-Zhao
    Yuan, Shi-Fang
    Jiang, Hua
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (15) : 15952 - 15971
  • [13] On Hermitian Solutions of the Split Quaternion Matrix Equation AXB plus CXD = E
    Yuan, Shi-Fang
    Wang, Qing-Wen
    Yu, Yi-Bin
    Tian, Yong
    ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2017, 27 (04) : 3235 - 3252
  • [14] A Hermitian least squares solution of the matrix equation AXB = C subject to inequality restrictions
    Li, Ying
    Gao, Yan
    Guo, Wenbin
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (06) : 1752 - 1760
  • [15] Relations between least-squares and least-rank solutions of the matrix equation AXB = C
    Tian, Yongge
    Wang, Hongxing
    APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (20) : 10293 - 10301
  • [16] Least squares solution of matrix equation AXB*+CYD*=E*
    Shim, SY
    Chen, Y
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (03) : 802 - 808
  • [17] Norm-constrained least-squares solutions to the matrix equation AXB=C
    Xu, Anbao
    Peng, Zhenyun
    PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE OF MATRICES AND OPERATORS (MAO 2012), 2012, : 136 - 139
  • [18] Least-squares solution with the minimum-norm for the matrix equation (AXB, GXH) = (C, D)
    Liao, AP
    Lei, Y
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 50 (3-4) : 539 - 549
  • [19] Least squares Toeplitzmatrix solutions of the matrix equation AXB plus CYD = F
    Yuan, Yongxin
    Zhao, Wenhua
    Liu, Hao
    LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (09) : 1867 - 1877
  • [20] Least-squares symmetric solution to the matrix equation AXB = C with the norm inequality constraint
    Xie, Dongxiu
    Xu, An-Bao
    Peng, Zhenyun
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2016, 93 (09) : 1564 - 1578
12345