ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi1 ; Huang, Yu-Mei2; Ng, Michael K.3
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| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2009 |
| 卷号 | 47期号:2页码:1019-1037 |
| 关键词 | time-dependent partial differential equation sinc-Galerkin discretization Toeplitz- like matrix preconditioning eigenvalue bound GMRES method |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/080718176 |
| 英文摘要 | When the Newton method or the fixed-point method is employed to solve the systems of nonlinear equations arising in the sinc-Galerkin discretization of certain time-dependent partial differential equations, in each iteration step we need to solve a structured subsystem of linear equations iteratively by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the tensor and the Toeplitz structures of the linear subsystems we construct structured preconditioners for their coefficient matrices and estimate the eigenvalue bounds of the preconditioned matrices under certain assumptions. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods. It has been shown that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is efficient and robust for solving the systems of nonlinear equations arising from the sinc-Galerkin discretization of the time-dependent partial differential equations. |
| 资助项目 | The National Basic Research Program[2005CB321702] ; The National Outstanding Young Scientist Foundation[10525102] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000265778900011 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/8157]  |
| 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, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Lanzhou Univ, Sch Informat Sci & Engn, Lanzhou 730000, Peoples R China 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Bai, Zhong-Zhi,Huang, Yu-Mei,Ng, Michael K.. ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2009,47(2):1019-1037. |
| APA | Bai, Zhong-Zhi,Huang, Yu-Mei,&Ng, Michael K..(2009).ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS.SIAM JOURNAL ON NUMERICAL ANALYSIS,47(2),1019-1037. |
| MLA | Bai, Zhong-Zhi,et al."ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS".SIAM JOURNAL ON NUMERICAL ANALYSIS 47.2(2009):1019-1037. |
入库方式： OAI收割
来源：数学与系统科学研究院
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