Cyclic gradient based iterative algorithm for a class of generalized coupled Sylvester-conjugate matrix equations |
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| Institution: | 1. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China;2. School of Mathematical Sciences, University of Jinan, Jinan 250022, China;1. School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China;2. School of Communication and Electronics, Jiangxi Science and Technology Normal University, Nanchang 330013, China;3. School of Mechano-electronic Engineering, Xidian University, Xi’an 710071, China;1. School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, PR China;2. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, PR China;3. Zhongguancun Laboratory, Beijing 100190, PR China;4. School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, PR China;5. Institute of Artificial Intelligence, Beihang University, Beijing 100191, PR China;1. Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan;2. Department of Electronics and Information Systems Engineering, Osaka Institute of Technology, Osaka, Japan;1. School of Astronautics, Beihang University, No.37 Xueyuan Road, Beijing 100191, PR China;2. Shanghai Institute of Satellite Engineering, No. 3666 Yuanjiang Road, Shanghai 201109, PR China;3. School of Astronautics, Northwestern Ploytechnical University (NWPU), No. 127 West Youyi Road, Xi’an, Shaanxi 710072, PR China;4. National Key Laboratory of Aerospace Flight Dynamics, NWPU, No. 127 West Youyi Road, Xi’an, Shaanxi 710072, PR China;1. School of Automation, Beijing Institute of Technology, Beijing, 100081, China;2. Faculty of Mechanical & Electrical Engineering, Kunming University of Science and Technology, Kunming, 650550, China |
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| Abstract: | This paper focuses on the numerical solution of a class of generalized coupled Sylvester-conjugate matrix equations, which are general and contain many significance matrix equations as special cases, such as coupled discrete-time/continuous-time Markovian jump Lyapunov matrix equations, stochastic Lyapunov matrix equation, etc. By introducing the modular operator, a cyclic gradient based iterative (CGI) algorithm is provided. Different from some previous iterative algorithms, the most significant improvement of the proposed algorithm is that less information is used during each iteration update, which is conducive to saving memory and improving efficiency. The convergence of the proposed algorithm is discussed, and it is verified that the algorithm converges for any initial matrices under certain assumptions. Finally, the effectiveness and superiority of the proposed algorithm are verified with some numerical examples. |
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