An efficient iterative method for solving the matrix equation AXB + CYD = E

Numerical Linear Algebra with Applications

Volumn 13, Issue 6, 2006, Pages 473-485

  Peng, Zhen Yun ^a,b   Peng, Ya Xin ^c  

^a HUNAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b CENTRAL SOUTH UNIVERSITY   (China)

^c HUNAN UNIVERSITY   (China)

Author keywords

Iterative method; Least norm solution; Matrix equation; Matrix nearness problem; Optimal approximation solution

Indexed keywords

EID: 33746904417     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.470     Document Type: Article

References (12)

1. Baksalary JK, Kala R. The matrix equation AXB + CYD = E. Linear Algebra and its Applications 1980; 30:141-147.
2. Peng Z-Y, Hu X-Y, Zhang L. The inverse problem of bisymmetric matrices with a submatrix constraint. Numerical Linear Algebra with Applications 2004; 11:59-73.
3. Chu KE. Singular value and generalized value decompositions and the solution of linear matrix equations. Linear Algebra and its Applications 1987; 87:83-98.
4. He C. The general solution of the matrix equation AXB+CYD = F. Acta Scientiarum Naturalium Universitatis Normalis Hunanensis, China 1996; 19:17-20 (in Chinese).
5. Xu G, Wei M, Zheng D. On solutions of matrix equation AXB + CYD = F. Linear Algebra and its Applications 1980; 279:93-109.
6. Peng Z-Y. The solutions of matrix equation AXC + BYD = E and its optimal approximation. Mathematics Theory and Applications 2002; 22(2):99-103 (in Chinese).
7. Shim S-Y, Chen Y. Least squares solution of matrix equation AXB* + CYD* = E. SIAM Journal on Matrix Analysis and Applications 2003; 3:8002-8008.
8. 2 = E. Journal of Jilin Institute of Chemical Technology 2003; 20(3):84-86 (in Chinese).
9. Baruch M. Optimization procedure to correct stiffness and flexibility matrices using vibration tests. American Institute of Aeronautics and Astronautics (AIAA) Journal 1978; 16:1208-1210.
10. Jeseph KT. Inverse eigenvalue problem in structural design. American Institute of Aeronautics and Astronautics (AIAA) Journal 1992; 30:2890-2896.
11. Jiang Z, Lu Q. Optimal application of a matrix under spectral restriction. Mathematica Numerica Sinica 1988; 1:47-52.
12. Higham NJ. Computing a nearest symmetric positive semidefinite matrix. Linear Algebra and its Applications 1988; 103:103-118.