ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi1 ; Guo, Xue-Ping2
|
| 刊名 | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 2010-03-01 |
| 卷号 | 28期号:2页码:235-260 |
| 关键词 | Systems of nonlinear equations HSS iteration method Newton method Local convergence |
| ISSN号 | 0254-9409 |
| DOI | 10.4208/jcm.2009.10-m2836 |
| 英文摘要 | The Hermitian and skew-Hermitian splitting (HSS) method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS iteration as the inner solver for the Newton method, we establish a class of Newton-HSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. For this class of inexact Newton methods, two types of local convergence theorems are proved under proper conditions, and numerical results are given to examine their feasibility and effectiveness. In addition, the advantages of the Newton-HSS methods over the Newton-USOR., the Newton-GMRES and the Newton-GCG methods are shown through solving Systems of nonlinear equations arising from the finite difference discretization of a two-dimensional convect ion-diffusion equation perturbed by a nonlinear term. The numerical implementations also show that as preconditioners for the Newton-GMRES and the Newton-GCG methods the HSS iteration outperforms the USOR iteration in both computing time and iteration step. |
| 资助项目 | National Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation, P.R. China[10471146] ; National Natural Science Foundation, P.R. China[10571059] ; National Natural Science Foundation, P.R. China[10571060] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000274262100005 |
| 出版者 | VSP BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/10342]  |
| 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, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China |
| 推荐引用方式 GB/T 7714 | Bai, Zhong-Zhi,Guo, Xue-Ping. ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2010,28(2):235-260. |
| APA | Bai, Zhong-Zhi,&Guo, Xue-Ping.(2010).ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES.JOURNAL OF COMPUTATIONAL MATHEMATICS,28(2),235-260. |
| MLA | Bai, Zhong-Zhi,et al."ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES".JOURNAL OF COMPUTATIONAL MATHEMATICS 28.2(2010):235-260. |
入库方式： OAI收割
来源：数学与系统科学研究院
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