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ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS
Dai, Hua1; Bai, Zhong-Zhi2
2011-05-01
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume29Issue:3Pages:341-366
AbstractWe 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.
KeywordDiscrete algebraic Riccati equation Symmetric positive definite solution Eigenvalue bound Fixed-point iteration Convergence theory
DOI10.4208/jcm.1010-m3258
Language英语
Funding ProjectLSEC ; National Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation for Innovative Research Groups, P.R. China[11021101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000291370000006
PublisherVSP BV
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12916
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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