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

doi:10.1137/060675344

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory
	Bai, Zhong-Zhi1 ; Gao, Yong-Hua 1; Lu, Lin-Zhang 2
刊名	SIAM JOURNAL ON SCIENTIFIC COMPUTING
	2008
卷号	30 期号:2 页码:804-818
关键词	nonsymmetric algebraic Riccati equation fixed-point equations in vector form splitting iteration method monotone convergence
ISSN号	1064-8275
DOI	10.1137/060675344
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000254461500012
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/6499]
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.