Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory

doi:10.1137/060675344

	Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory
	Bai, Zhong-Zhi1 ; Gao, Yong-Hua 1; Lu, Lin-Zhang 2
	2008
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	30 期号:2 页码:804-818
摘要	For a class of nonsymmetric algebraic Riccati equations arising from transport theory, Lu [SIAM J. Matrix Anal. Appl., 26 (2005), pp. 679-685] reformulated them into a couple of fixed-point equations in a vector form and constructed an iterative method for finding their minimal positive solutions. In this paper, based on this fixed-point equation, we propose several fast and effective iterative methods for solving the above-mentioned special type of nonsymmetric algebraic Riccati equations. These iterative methods can be categorized into the class of nonlinear block relaxation iterations and can also be considered as accelerated variants of the known fixed-point iteration according to the principle of using the currently available information as promptly as possible. The monotone convergence theorems about these new iterative methods are established, and the sharper bounds about the solutions of the nonsymmetric algebraic Riccati equations are derived. Numerical implementations show that the new iterative methods are feasible and effective solvers for the nonsymmetric algebraic Riccati equations arising from transport theory.
关键词	nonsymmetric algebraic Riccati equation fixed-point equations in vector form splitting iteration method monotone convergence
DOI	10.1137/060675344
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000254461500012
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6500
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.Xiamen Univ, Sch Math Sci, Dept Informat & Computat Math, Xiamen 361005, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Gao, Yong-Hua,Lu, Lin-Zhang. Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2008,30(2):804-818.
APA	Bai, Zhong-Zhi,Gao, Yong-Hua,&Lu, Lin-Zhang.(2008).Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory.SIAM JOURNAL ON SCIENTIFIC COMPUTING,30(2),804-818.
MLA	Bai, Zhong-Zhi,et al."Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory".SIAM JOURNAL ON SCIENTIFIC COMPUTING 30.2(2008):804-818.