On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations |
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| Institution: | 1. School of Mathematics and Statistics & FJKLMAA, Fujian Normal University, Fuzhou 350117, PR China;2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China;1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China;1. Department of Systems and Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, PR China;2. School of Mechanical and Mechatronic Engineering, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, Australia;3. College of Mathematics and Computer Science, Changsha UniversityChangsha, Hunan 410022, PR China;4. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114, China;1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China;2. Doctoral School FEIT, SS Cyril and Methodius University, 18 Rugjer Boskovic Str, Karpos 2, Skopje 1000, Republic of N. Macedonia;1. School of Computer Science and School of Cyberspace Science Xiangtan University, Xiangtan, 411105, PR China;2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, PR China;3. School of Mathematics Science, Liaocheng University, Liaocheng, 252000, PR China;1. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, 210023, People’s Republic of China;2. Faculty of Information and Technology, Beijing University of Technology, Beijing, 100124, China;3. School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, 610106, China;4. School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China;5. Key Laboratory of HPC-SIP (MOE), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, China;1. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China;2. Guangdong Key Laboratory of Modern Control Technology, Guangzhou 510070, China;3. Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, Guangzhou 510006, China |
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| Abstract: | In this paper, we propose the full-rank and reduced-rank relaxed gradient-based iterative algorithms for solving the generalized coupled Sylvester-transpose matrix equations. We provide analytically the necessary and sufficient condition for the convergence of the proposed iterative algorithm and give explicitly the optimal step size such that the convergence rate of the algorithm is maximized. Some numerical examples are examined to confirm the feasibility and efficiency of the proposed algorithms. |
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