ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS

doi:10.4208/jcm.1010-m3258

	ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS
	Dai, Hua 1; Bai, Zhong-Zhi2
	2011-05-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	29 期号:3 页码:341-366
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.
关键词	Discrete algebraic Riccati equation Symmetric positive definite solution Eigenvalue bound Fixed-point iteration Convergence theory
DOI	10.4208/jcm.1010-m3258
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000291370000006
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12916
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.