SIAM Journal on Matrix Analysis and Applications
Parallel computation of the solutions of coupled algebraic Lyapunov equations
Automatica (Journal of IFAC)
Matrix computations (3rd ed.)
Generalized Reflexive Matrices: Special Properties and Applications
SIAM Journal on Matrix Analysis and Applications
Fast algorithms for the Sylvester equation AX − XBT = C
Theoretical Computer Science
On Iterative Solutions of General Coupled Matrix Equations
SIAM Journal on Control and Optimization
A new projection method for solving large Sylvester equations
Applied Numerical Mathematics
Solutions to generalized Sylvester matrix equation by Schur decomposition
International Journal of Systems Science
Use of near-breakdowns in the block Arnoldi method for solving large Sylvester equations
Applied Numerical Mathematics
The reflexive solutions of the matrix equation AX B = C
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Weighted least squares solutions to general coupled Sylvester matrix equations
Journal of Computational and Applied Mathematics
The solvability conditions for the inverse eigenvalue problems of reflexive matrices
Journal of Computational and Applied Mathematics
Hierarchical gradient-based identification of multivariable discrete-time systems
Automatica (Journal of IFAC)
Computers & Mathematics with Applications
An efficient algorithm for solving general coupled matrix equations and its application
Mathematical and Computer Modelling: An International Journal
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The generalised coupled Sylvester matrix equations [image omitted] [image omitted] with unknown matrices X and Y, have important applications in control and system theory. Also it is well known that the reflexive and anti-reflexive matrices have wide applications in many fields. In this article, we consider the generalised coupled Sylvester matrix equations over reflexive and anti-reflexive matrices. First we propose two new matrix equations equivalent to the generalised coupled Sylvester matrix equations over reflexive and anti-reflexive matrices, respectively. Then two new iterative algorithms are proposed for solving these matrix equations. The convergence analysis of the proposed iterative algorithms is derived. Finally, some numerical examples are presented to illustrate the theoretical results of this article.