Weighted least squares solutions to general coupled Sylvester matrix equations

Journal of Computational and Applied Mathematics

Volumn 224, Issue 2, 2009, Pages 759-776

  Zhou, Bin ^a   Li, Zhao Yan ^a   Duan, Guang Ren ^a   Wang, Yong ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Coupled Sylvester matrix equations; Gradient based iterative algorithms; Maximal convergence rate; Weighted generalized inverses; Weighted least squares solutions

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; CURVE FITTING; DATA FUSION; INVERSE PROBLEMS; LEAST SQUARES APPROXIMATIONS; PAPER; SENSOR DATA FUSION; TRAJECTORIES;

COUPLED SYLVESTER MATRIX EQUATIONS; GRADIENT BASED ITERATIVE ALGORITHMS; MAXIMAL CONVERGENCE RATE; WEIGHTED GENERALIZED INVERSES; WEIGHTED LEAST SQUARES SOLUTIONS;

ITERATIVE METHODS;

EID: 58149346165     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.06.014     Document Type: Article

References (30)

1. Wang D. Some topics on weighted Moore-Penrose inverse, weighted least squares and weighted regularized Tikhonov problems. Applied Mathematics and Computation 157 (2004) 243-267
2. Ki{dotless}li{dotless}cman A., and Abdel Aziz Al Zhour Z. Vector least-squares solutions for coupled singular matrix equations. Journal of Computational and Applied Mathematics 206 (2007) 1051-1069
3. Zhou B., and Duan G.R. An explicit solution to the matrix equation A X - X F = B Y. Linear Algebra and its Applications 402 1 (2005) 345-366
4. Zhou B., and Duan G.R. A new solution to the generalized Sylvester matrix equation A V - E V F = B W. Systems & Control Letters 55 3 (2006) 193-198
5. 2 + D V F + K V = B W. IEEE Transactions on Automatic Control 51 5 (2006) 805-809
6. Zhou B., and Duan G.R. On the generalized Sylvester mapping and matrix equations. Systems & Control Letters 57 3 (2008) 200-208
7. Zhou B., and Duan G.R. Solutions to generalized Sylvester matrix equation by Schur decomposition. International Journal of Systems Science 38 5 (2007) 369-375
8. l = C. Linear Algebra and its Applications 426 (2007) 583-595
9. T. Stykel, Solving projected generalized Lyapunov equations using SLICOT, in: 2006 IEEE International Symposium on Computer-Aided Control Systems Design, pp. 14-18
10. Chen T., and Francis B.A. Optimal Sampled-date Control Systems (1995), Springer, Londom
11. Costa O.L.V., and Fragoso M.D. Stability results for discrete-time linear systems with Markovian jumping parameters. Journal of Mathematical Analysis and Applications 179 1 (1993) 154-178
12. Borno I., and Gajic Z. Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems. Computers and Mathematics with Applications 30 7 (1995) 1-4
13. Wang Q., Lam J., Wei Y., and Chen T. Iterative solutions of coupled discrete Markovian jump Lyapunov equations. Computers and Mathematics with Applications 55 4 (2008) 843-850
14. Chen J.L., and Chen X.H. Special Matrices (2002), Tsinghua University Press (in Chinese)
15. Kelley C.T. Iterative Methods for Linear and Nonlinear Equations (1995), SIAM, Philadelphia
16. Zhou K., Doyle J., and Glover K. Robust and Optimal Control (1996), Prentice-Hell
17. Mouroutsos G., and Sparis P.D. Taylor series approach to system identification, analysis and optimal control. Journal of Franklin Institute Pergamon 319 3 (1985) 359-371
18. Huang G.X., Yin F., and Guo K. An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation A X B = C. Journal of Computational and Applied Mathematics 212 2 (2008) 231-244
19. H X B = C. Journal of Computational and Applied Mathematics 200 2 (2007) 749-760
20. Thiran J.P., Matelart M., and Le Bailly B. On the generalized ADI method for the matrix equation X - A X B = C. Journal of Computational and Applied Mathematics 156 2 (2003) 285-302
21. Ding F., and Chen T. On iterative solutions of general coupled matrix equations. SIAM Journal on Control and Optimization 44 6 (2006) 2269-2284
22. Ding F., Liu P.X., and Ding J. Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. Applied Mathematics and Computation 197 1 (2008) 41-50
23. Ding F., and Chen T. Gradient based iterative algorithms for solving a class of matrix equations. IEEE Transactions on Automatic Control 50 8 (2005) 1216-1221
24. Ding F., and Chen T. Iterative least squares solutions of coupled Sylvester matrix equations. Systems and Control Letters 54 2 (2005) 95-107
25. Sheng X.P., and Chen G.L. A finite iterative method for solving a pair of linear matrix equations (A X B, C X D) = (E, F). Applied Mathematics and Computation 189 (2007) 1350-1358
26. Peng Z.Y. An iterative method for the least squares symmetric solution of the linear matrix equation A X B = C. Applied Mathematics and Computation 170 (2005) 711-723
27. 2. Applied Mathematics and Computation 181 (2006) 988-999
28. T = F with some linear constraints. Applied Mathematics and Computation 185 (2007) 284-300
29. De Pierro A.R., and Wei M. Some new properties of the equality constrained and weighted least squares problem. Linear Algebra and Its Applications 320 (2000) 145-165
30. Wang G.R., and Zheng B. The weighted generalized inverses of a partitioned matrix. Linear Algebra and Its Applications 320 (2000) 145-165