Factor gradient iterative algorithm for solving a class of discrete periodic Sylvester matrix equations |
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| Institution: | 1. School of Mathematics and Statistics & FJKLMAA, Fujian Normal University, Fuzhou 350117, PR China;2. School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202, PR China;1. Dep. of Systems and Automation Engineering, University of Seville, Seville, 41092, Spain;2. Dep. of Engineering, Loyola University Andalusia, Dos Hermanas, Seville, 41704, Spain;1. College of Engineering University of Hail Po.Box 2440, Hail, Kingdom of Saudi Arabia;2. National School of Engineering of Sfax, University of Sfax, Lab-STA, LR11ES50, 3038, Sfax, Tunisia;3. Modeling, Information, and Systems Laboratory, University of Picardie Jules Verne, UFR of Sciences, 33 Rue St Leu Amiens 80000, France;1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410000, China;2. School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518055, China;3. Shenzhen Key Laboratory of Visual Object Detection and Recognition, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China;4. School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518055, 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. School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China;2. College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China |
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| Abstract: | At present, gradient iteration methods have been used to solve various Sylvester matrix equations and proved effective. Based on this method, we generalize the factor gradient iterative method (FGI) for solving forward periodic Sylvester matrix equations (FPSME) and backward periodic Sylvester matrix equations (BPSME). To accelerate the convergence of the iterative method, we refer to Gauss-Seidel and Jacobi iterative construction ideas and use the latest matrix information in the FGI iterative method to obtain the modified factor gradient iterative (MFGI) method. Then, the convergence of the proposed methods and the selection of optimal factors are proved. The last numerical examples illustrate the effectiveness and applicability of the iterative methods. |
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