On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations

doi:10.1002/nla.727

	On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations
	Gao, Yong-Hua 1,2; Bai, Zhong-Zhi1
	2011-05-01
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
卷号	18 期号:3 页码:325-341
摘要	Newton 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.
关键词	non-symmetric algebraic Riccati equation M-matrix Newton iteration method doubling iteration scheme inexact iteration convergence
DOI	10.1002/nla.727
语种	英语
资助项目	The National Basic Research Program[2005CB321702] ; The National Outstanding Young Scientist Foundation[10525102] ; The National Natural Science Foundation, P. R. China[10471146]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000290162800004
出版者	WILEY-BLACKWELL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12518
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	1.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
推荐引用方式 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.