Robust and optimal control
Optimal Sampled-Data Control Systems
Optimal Sampled-Data Control Systems
On the generalized ADI method for the matrix equation X -AXB = C
Journal of Computational and Applied Mathematics
On Iterative Solutions of General Coupled Matrix Equations
SIAM Journal on Control and Optimization
The reflexive and anti-reflexive solutions of the matrix equation AHXB=C
Journal of Computational and Applied Mathematics
Vector least-squares solutions for coupled singular matrix equations
Journal of Computational and Applied Mathematics
Solutions to generalized Sylvester matrix equation by Schur decomposition
International Journal of Systems Science
Journal of Computational and Applied Mathematics
Iterative solutions of coupled discrete Markovian jump Lyapunov equations
Computers & Mathematics with Applications
Iterative solutions to matrix equations of the form AiXBi=Fi
Computers & Mathematics with Applications
Matrix equations over (R,S)-symmetric and (R,S)-skew symmetric matrices
Computers & Mathematics with Applications
Iterative solutions to coupled Sylvester-conjugate matrix equations
Computers & Mathematics with Applications
On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations
International Journal of Systems Science
On the global Krylov subspace methods for solving general coupled matrix equations
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
Eigenstructure assignment for linear parameter-varying systems with applications
Mathematical and Computer Modelling: An International Journal
An efficient algorithm for solving general coupled matrix equations and its application
Mathematical and Computer Modelling: An International Journal
Efficient iterative solutions to general coupled matrix equations
International Journal of Automation and Computing
Developing Bi-CG and Bi-CR methods to solve generalized Sylvester-transpose matrix equations
International Journal of Automation and Computing
Hi-index | 7.29 |
This paper is concerned with weighted least squares solutions to general coupled Sylvester matrix equations. Gradient based iterative algorithms are proposed to solve this problem. This type of iterative algorithm includes a wide class of iterative algorithms, and two special cases of them are studied in detail in this paper. Necessary and sufficient conditions guaranteeing the convergence of the proposed algorithms are presented. Sufficient conditions that are easy to compute are also given. The optimal step sizes such that the convergence rates of the algorithms, which are properly defined in this paper, are maximized and established. Several special cases of the weighted least squares problem, such as a least squares solution to the coupled Sylvester matrix equations problem, solutions to the general coupled Sylvester matrix equations problem, and a weighted least squares solution to the linear matrix equation problem are simultaneously solved. Several numerical examples are given to illustrate the effectiveness of the proposed algorithms.