A Riccati transformation method for solving linear BVPs. I: theoretical aspects
SIAM Journal on Numerical Analysis
Iterative solution of the Lyapunov matrix equation
Applied Mathematics Letters
ACM Transactions on Mathematical Software (TOMS)
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Generalized Reflexive Matrices: Special Properties and Applications
SIAM Journal on Matrix Analysis and Applications
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Matrix Analysis and Applications
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
Computers & Mathematics with Applications
Weighted least squares solutions to general coupled Sylvester matrix equations
Journal of Computational and Applied Mathematics
Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
Computers & Mathematics with Applications
The general solution to a system of real quaternion 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
Hierarchical gradient-based identification of multivariable discrete-time systems
Automatica (Journal of IFAC)
Mathematical and Computer Modelling: An International Journal
Matrix equations over (R,S)-symmetric and (R,S)-skew symmetric matrices
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
Parameter estimation for nonlinear dynamical adjustment models
Mathematical and Computer Modelling: An International Journal
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The general coupled matrix equations (I){A"1"1X"1B"1"1+A"1"2X"2B"1"2+...+A"1"lX"lB"1"l=C"1,A"2"1X"1B"2"1+A"2"2X"2B"2"2+...+A"2"lX"lB"2"l=C"2,@?A"l"1X"1B"l"1+A"l"2X"2B"l"2+...+A"l"lX"lB"l"l=C"l, (including the generalized coupled Sylvester matrix equations as special cases) have nice applications in various branches of control and system theory. In this paper, by extending the idea of conjugate gradient method, we propose an efficient iterative algorithm to solve the general coupled matrix equations (I). When the matrix equations (I) are consistent, for any initial matrix group, a solution group can be obtained within finite iteration steps in the absence of roundoff errors. The least Frobenius norm solution group of the general coupled matrix equations can be derived when a suitable initial matrix group is chosen. We can use the proposed algorithm to find the optimal approximation solution group to a given matrix group (X@^"1,X@^"2,...,X@^"l) in a Frobenius norm within the solution group set of the matrix equations (I). Also several numerical examples are given to illustrate that the algorithm is effective. Furthermore, the application of the proposed algorithm for solving the system of matrix equations {D"1XE"1=F"1,@?D"pXE"p=F"p, over (R,S)-symmetric and (R,S)-skew symmetric matrices is highlighted.