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On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations
Gao, Yong-Hua1,2; Bai, Zhong-Zhi1
2011-05-01
Source PublicationNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN1070-5325
Volume18Issue:3Pages:325-341
AbstractNewton iteration method can be used to find the minimal non-negative solution of a certain class of non-symmetric algebraic Riccati equations. However, a serious bottleneck exists in efficiency and storage for the implementation of the Newton iteration method, which comes from the use of some direct methods in exactly solving the involved Sylvester equations. In this paper, instead of direct methods, we apply a fast doubling iteration scheme to inexactly solve the Sylvester equations. Hence, a class of inexact Newton iteration methods that uses the Newton iteration method as the outer iteration and the doubling iteration scheme as the inner iteration is obtained. The corresponding procedure is precisely described and two practical methods of monotone convergence are algorithmically presented. In addition, the convergence property of these new methods is studied and numerical results are given to show their feasibility and effectiveness for solving the non-symmetric algebraic Riccati equations. Copyright (C) 2010 John Wiley & Sons, Ltd.
Keywordnon-symmetric algebraic Riccati equation M-matrix Newton iteration method doubling iteration scheme inexact iteration convergence
DOI10.1002/nla.727
Language英语
Funding ProjectThe National Basic Research Program[2005CB321702] ; The National Outstanding Young Scientist Foundation[10525102] ; The National Natural Science Foundation, P. R. China[10471146]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000290162800004
PublisherWILEY-BLACKWELL
Citation statistics
Cited Times:20[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12518
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.CNPC, CNPC Explorat Software Corp Ltd, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Gao, Yong-Hua,Bai, Zhong-Zhi. On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2011,18(3):325-341.
APA Gao, Yong-Hua,&Bai, Zhong-Zhi.(2011).On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,18(3),325-341.
MLA Gao, Yong-Hua,et al."On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 18.3(2011):325-341.
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