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Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory
Bai, Zhong-Zhi1; Gao, Yong-Hua1; Lu, Lin-Zhang2
2008
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume30Issue:2Pages:804-818
AbstractFor 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.
Keywordnonsymmetric algebraic Riccati equation fixed-point equations in vector form splitting iteration method monotone convergence
DOI10.1137/060675344
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000254461500012
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/6500
Collection计算数学与科学工程计算研究所
Corresponding AuthorBai, Zhong-Zhi
Affiliation1.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
Recommended Citation
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.
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