Convergence analysis of Newton method without inversion for solving discrete algebraic Riccati equations |
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| Affiliation: | 1. Faculty of Mathematics and Statistics, Malayer University, Malayer, Iran;2. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran;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. College of Mathematics and Computer Science, Tongling University, Tongling, 244000, China;2. School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, 212013, China;1. National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, 401331, PR China;2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, PR China;3. Faculty of Engineering and IT, University of Technology Sydney, NSW 2007, Australia;4. School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200072, PR China;1. Institute for Mathematics, University of Würzburg, Emil-Fischer-Straße 40, Würzburg 97074, Germany;2. Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Campus, 65080, Van-Turkey;1. College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, PR China;2. College of Biological and Chemical engineering, Guangxi University of Science and Technology, Liuzhou 545006, PR China;3. College of Mathematics, Suzhou University of Science and Technology, Suzhou 215009, PR China;4. Department of Economics, The Chinese University of Hong Kong, Hong Kong, PR China;1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;2. Research Center of Semi-tensor Product of Matrices, Theory and Applications, Liaocheng University, Lianocheng, PR China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China |
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| Abstract: | In this paper, we first introduce the necessary and sufficient conditions for the existence of the solution of discrete algebraic Riccati equation. Then we propose the Newton method without inversion to find the solution of the discrete algebraic Riccati equation. We show that the proposed method converges to a positive definite solution of the discrete algebraic Riccati equation. Finally, the accuracy and effectiveness of the proposed method in compare to some existing algorithms are demonstrated by various numerical examples. |
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