Iterative algorithms for the minimum-norm solution and the least-squares solution of the linear matrix equations A1XB1 + C 1XTD1 = M1, A2XB 2 + C2XTD2 = M2

Applied Mathematics and Computation

Volumn 218, Issue 7, 2011, Pages 3166-3175

  Liang, Kaifu ^a   Liu, Jianzhou ^a  

^a XIANGTAN UNIVERSITY   (China)

Author keywords

Iterative method; Least squares solution; Matrix equations; Minimum norm solution; Optimal approximation solution

Indexed keywords

INITIAL VALUES; ITERATIVE ALGORITHM; LEAST SQUARES SOLUTIONS; LINEAR MATRIX EQUATIONS; MATRIX; MATRIX EQUATIONS; MINIMUM NORM SOLUTIONS; NUMERICAL EXAMPLE; OPTIMAL APPROXIMATION;

ALGORITHMS; ITERATIVE METHODS; OPTIMIZATION;

MATRIX ALGEBRA;

EID: 80054969557     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.08.052     Document Type: Article

References (24)

1. C2 with applications Comput. Math. Appl. 41 2001 929 935
2. AiXBj = C, (i, j) ∈ Γ Linear Algebr. Appl. 375 2003 135 145
3. P. Bhimasankaram Common solutions to the linear matrix equations AX = B, CX = D, and EXF = G Sankhya Ser. A 38 1976 404 409
4. S.K. Mitra the matrix equations AX = C, XB = D Linear Algebr. Appl. 59 1984 171 181
5. C2 and a matrix programming problem Linear Algebr. Appl. 131 1990 107 123
6. Y.X. Peng, X.Y. Hu, and L. Zhang An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C Appl. Math. Comput. 160 2005 763 777
7. C2 Appl. Math. Comput. 183 2006 1127 1137
8. C2 Math. Comput. Model. 50 2009 1237 1244
9. A.P. Liao, and Y. Lei Least-squares solution with the minimum-norm for the matrix equation (AXB, GXH) = (C, D) Comput. Math. Appl. 50 2005 539 549
10. M. Dehdi, and M. Hajarian An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation Appl. Math. Comput. 202 2008 571 588
11. CXTD = E Appl. Math. Comput. 187 2007 622 629
12. F. Ding, and T. Chen Iterative least-squares solutions of coupled Sylvester matrix equations Syst. Control Lett. 54 2 2005 95 107
13. F. Ding, and T. Chen On iterative solutions of general coupled matrix equations SIAM J. Control Optim. 44 6 2006 2269 2284
14. F. Ding, and T. Chen Gradient based iterative algorithms for solving a class of matrix equations IEEE T. Automat. Control 50 8 2005 1216 1221
15. R.A. Horn, and C.R. Johnson Topics in Matrix Analysis 1991 Cambridge University Press pp. 259-260
16. Z. Al Zhour, and A. kilicman Some new connections between matrix products for partitioned and non-partitioned matrices Comput. Math. Appl. 54 2007 763 784
17. CXTD = F Appl. Math. Comput. 217 5 2010 2191 2199
18. L. Xie, J. Ding, and F. Ding Gradient based iterative solutions for general linear matrix equations Comput. Math. Appl. 58 7 2009 1441 1448
19. Fi Comput. Math. Appl. 59 11 2010 3500 3507
20. F. Ding, P.X. Liu, and J. Ding Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle Appl. Math. Comput. 197 1 2008 41 50
21. L.Y. Wang, L. Xie, and X.F. Wang The residual based interactive stochastic gradient algorithms for controlled moving average models Appl. Math. Comput. 211 2 2009 442 449
22. Y.J. Liu, Y.S. Xiao, and X.L. Zhao Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model Appl. Math. Comput. 215 4 2009 1477 1483
23. F. Ding, L. Qiu, and T. Chen Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems Automatica 45 2 2009 324 332
24. F. Ding, G. Liu, and P.X. Liu Partially coupled stochastic gradient identification methods for non-uniformly sampled systems IEEE T. Automat. Control 55 8 2010 1976 1981