Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations

doi:10.1002/nla.500

	Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations
	Bai, Zhong-Zhi; Guo, Xiao-Xia ; Xu, Shu-Fang
	2006-10-01
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
卷号	13 期号:8 页码:655-674
摘要	For the non-symmetric algebraic Riccati equations, we establish a class of alternately linearized implicit (ALI) iteration methods for computing its minimal non-negative solutions by technical combination of alternate splitting and successive approximating of the algebraic Riccati operators. These methods include one iteration parameter, and suitable choices of this parameter may result in fast convergent iteration methods. Under suitable conditions, we prove the monotone convergence and estimate the asymptotic convergence factor of the ALI iteration matrix sequences. Numerical experiments show that the ALI iteration methods are feasible and effective, and can outperform the Newton iteration method and the fixed-point iteration methods. Besides, we further generalize the known fixed-point iterations, obtaining an extensive class of relaxed splitting iteration methods for solving the non-symmetric algebraic Riccati equations. Copyright (C) 2006 John Wiley & Sons, Ltd.
关键词	non-symmetric algebraic Riccati equation minimal non-negative solution M-matrix alternately linearized iteration monotone convergence
DOI	10.1002/nla.500
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000241089100004
出版者	JOHN WILEY & SONS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3495
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, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Guo, Xiao-Xia,Xu, Shu-Fang. Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2006,13(8):655-674.
APA	Bai, Zhong-Zhi,Guo, Xiao-Xia,&Xu, Shu-Fang.(2006).Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,13(8),655-674.
MLA	Bai, Zhong-Zhi,et al."Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 13.8(2006):655-674.