Global-DGMRES method for matrix equation AXB = C

被引：4
|
作者：
Safarzadeh, Malihe [1 ]
Sadeghi Goughery, Hossein [1 ]
Salemi, Abbas [2 ,3 ]
机构：
[1] Islamic Azad Univ, Kerman Branch, Dept Math, Kerman, Iran
[2] Shahid Bahonar Univ Kerman, Dept Appl Math, Kerman, Iran
[3] Shahid Bahonar Univ Kerman, Mahani Math Res Ctr, Kerman, Iran
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2022年 / 99卷 / 05期
关键词：
Matrix equations; global-DGMRES method; drazin inverse solution; matrix Krylov subspaces; deblurring problems; KRYLOV SUBSPACE METHODS; DRAZIN-INVERSE SOLUTION; GENERAL LINEAR-SYSTEMS; REGULARIZATION METHODS;
D O I：
10.1080/00207160.2021.1942459
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a new algorithm Global-DGMRES to find the Drazin inverse solution of the linear matrix equation AXB = C, where at least one of the matrices A or B is rank deficient. This method is based on oblique projection process, onto matrix Krylov subspaces. Also, we study convergence properties of this algorithm. The matrix equation AXB = C is a mathematical model for deblurring problems and the Global-DGMRES method helps us to reconstruct blurred images corresponding to this matrix equation. Moreover, by numerical results, we compare the proposed method with Global-LSMR and Global-LSQR.
引用
收藏
页码：1005 / 1021
页数：17
相关论文
共 50 条
  • [31] SOLVING THE MATRIX INEQUALITY AXB plus (AXB)* ≥ C
    Tian, Yongge
    von Rosen, Dietrich
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2012, 15 (03): : 537 - 548
  • [32] On solutions of matrix equation AXB=C under semi-tensor product
    Ji, Zhen-dong
    Li, Jiao-fen
    Zhou, Xue-lin
    Duan, Fu-jian
    Li, Tao
    LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (10): : 1935 - 1963
  • [33] Optimal approximate solution of the matrix equation AXB = C over symmetric matrices
    College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
    J Comput Math, 2007, 5 (543-552):
  • [34] A new method for solving matrix equation = AXB+CXT D=E
    Wang, Minghui
    Mathematical and Computational Applications, 2013, 18 (01) : 12 - 18
  • [35] An efficient iterative method for solving the matrix equation AXB plus CYD = E
    Peng, Zhen-yun
    Peng, Ya-xin
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2006, 13 (06) : 473 - 485
  • [36] On the rank range of the least-squares solutions of the matrix equation AXB=C
    Meng, Chun-Jun
    Li, Tao-Zhen
    Hunan Daxue Xuebao/Journal of Hunan University Natural Sciences, 2013, 40 (07): : 92 - 94
  • [37] RANKS AND INDEPENDENCE OF SOLUTIONS OF THE MATRIX EQUATION AXB
    Tian, Yongge
    ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2006, 75 (01): : 75 - 84
  • [38] A real representation method for special least squares solutions of the quaternion matrix equation (AXB, DXE) = (C, F)
    Zhang, Fengxia
    Li, Ying
    Zhao, Jianli
    AIMS MATHEMATICS, 2022, 7 (08): : 14595 - 14613
  • [39] OPTIMAL APPROXIMATE SOLUTION OF THE MATRIX EQUATION AXB = C OVER SYMMETRIC MATRICES
    Anping Liao and Yuan Lei College of Mathematics and Econometrics
    Journal of Computational Mathematics, 2007, (05) : 543 - 552
  • [40] Optimal approximate solution of the matrix equation AXB = C over symmetric matrices
    Liao, Anping
    Lei, Yuan
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2007, 25 (05) : 543 - 552
12345