Conjugate gradient-based iterative algorithm for solving generalized periodic coupled Sylvester matrix equations |
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| Institution: | 1. Graduate College, Air Force Engineering University, Xi’an 710038, China;2. Aeronautics Engineering College, Air Force Engineering University, Xi’an 710038, China;3. National Innovation Institute of Defense Technology, Beijing 100071, China;1. College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China;2. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;1. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, China;2. School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China;1. Key Laboratory of Networks and Cloud Computing Security of Universities in Chongqing, School of Electronic and Information Engineering, Southwest University, Chongqing, China;2. School of Cyberspace Security, Beijing Institute of Technology, Beijing, China |
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| Abstract: | This paper focuses on constructing a conjugate gradient-based (CGB) method to solve the generalized periodic coupled Sylvester matrix equations in complex space. The presented method is developed from a point of conjugate gradient methods. It is proved that the presented method can find the solution of the considered matrix equations within finite iteration steps in the absence of round-off errors by theoretical derivation. Some numerical examples are provided to verify the convergence performance of the presented method, which is superior to some existing numerical algorithms both in iteration steps and computation time. |
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