An iterative scheme for a class of generalized Sylvester matrix equations

نویسندگان
Dehghan, Mehdi ID 1
Karamali, Gholamreza ID 2
Shirilord, Akbar ID 3

1 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

2 Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology, South Mehrabad, Tehran, Iran

3 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

doi
10.22060/ajmc.2024.22444.1159
چکیده

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.

کلیدواژه‌ها
Optimal parameters, Complex matrices, Generalized Sylvester matrix equation, Accelerated over relaxation (AOR) method, control theory