KMS Of Academy of mathematics and systems sciences, CAS
On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations | |
Gao, Yong-Hua1,2; Bai, Zhong-Zhi1 | |
2011-05-01 | |
Source Publication | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
ISSN | 1070-5325 |
Volume | 18Issue:3Pages:325-341 |
Abstract | 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. |
Keyword | non-symmetric algebraic Riccati equation M-matrix Newton iteration method doubling iteration scheme inexact iteration convergence |
DOI | 10.1002/nla.727 |
Language | 英语 |
Funding Project | The National Basic Research Program[2005CB321702] ; The National Outstanding Young Scientist Foundation[10525102] ; The National Natural Science Foundation, P. R. China[10471146] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000290162800004 |
Publisher | WILEY-BLACKWELL |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/12518 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Bai, Zhong-Zhi |
Affiliation | 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 |
Recommended Citation 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. |
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