An iterative scheme for a class of generalized Sylvester matrix equations

Abstract

In this study based on the accelerated over relaxation (AOR) method we make an iterative scheme for solving generalized Lyapunov matrix equation$$ {A}{X}+{X}{B}+\sum_{j=1}^{m}{N}_j{X}{M}_j={C},$$over complex or real matrices. Then we analyze the convergence of the new iterative method in detail. There have been discussions for the calculation of optimal parameters. Finally a numerical example is given to demonstrate the capability of the new method.

Keywords

• optimal parameters
• complex matrices
• generalized sylvester matrix equation
• accelerated over relaxation (aor) method
• control theory