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ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS

文献类型：期刊论文

作者Dai, Hua1; Bai, Zhong-Zhi2
刊名JOURNAL OF COMPUTATIONAL MATHEMATICS
出版日期2011-05-01
卷号29期号:3页码:341-366
关键词Discrete algebraic Riccati equation Symmetric positive definite solution Eigenvalue bound Fixed-point iteration Convergence theory
ISSN号0254-9409
DOI10.4208/jcm.1010-m3258
英文摘要We derive new and tight bounds about the eigenvalues and certain sums of the eigenvalues for the unique symmetric positive definite solutions of the discrete algebraic Riccati equations. These bounds considerably improve the existing ones and treat the cases that have been not discussed in the literature. Besides, they also result in completions for the available bounds about the extremal eigenvalues and the traces of the solutions of the discrete algebraic Riccati equations. We study the fixed-point iteration methods for computing the symmetric positive definite solutions of the discrete algebraic Riccati equations and establish their general convergence theory. By making use of the Schulz iteration to partially avoid computing the matrix inversions, we present effective variants of the fixed-point iterations, prove their monotone convergence and estimate their asymptotic convergence rates. Numerical results show that the modified fixed-point iteration methods are feasible and effective solvers for computing the symmetric positive definite solutions of the discrete algebraic Riccati equations.
资助项目LSEC ; National Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation for Innovative Research Groups, P.R. China[11021101]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000291370000006
出版者VSP BV
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/12915]  
专题计算数学与科学工程计算研究所
通讯作者Dai, Hua
作者单位1.Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Dai, Hua,Bai, Zhong-Zhi. ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2011,29(3):341-366.
APA Dai, Hua,&Bai, Zhong-Zhi.(2011).ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS.JOURNAL OF COMPUTATIONAL MATHEMATICS,29(3),341-366.
MLA Dai, Hua,et al."ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS".JOURNAL OF COMPUTATIONAL MATHEMATICS 29.3(2011):341-366.

入库方式： OAI收割

来源：数学与系统科学研究院

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