A note on the convergence of the two-grid method for Toeplitz systems
文献类型：期刊论文
| 作者 | Sun, HW; Chan, RH; Chang, QS |
| 刊名 | COMPUTERS & MATHEMATICS WITH APPLICATIONS
 |
| 出版日期 | 1997-07-01 |
| 卷号 | 34期号:1页码:11-18 |
| 关键词 | multigrid method Toeplitz matrices Richardson method damped-Jacobi method |
| ISSN号 | 0898-1221 |
| 英文摘要 | In this paper, we consider solutions of Toeplitz systems Au = b where the Toeplitz matrices A are generated by nonnegative functions with zeros. Since the matrices A are ill-conditioned, the convergence factor of classical iterative methods, such as the Richardson method, will approach 1 as the size n of the matrices becomes large. In [1,2], convergence of the two-grid method with Richardson method as smoother was proved for band tau matrices and it was conjectured that this convergence result can be carried to Toeplitz systems. In this paper, we show that the two-grid method with Richardson smoother indeed converges for Toeplitz systems that are generated by functions with zeros, provided that the order of the zeros are less than or equal to 2. However, we illustrate by examples that the convergence results of the two-grid method cannot be readily extended to multigrid method for n that are not of the form 2(l) - 1. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:A1997XR83800002 |
| 出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/29033]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Sun, HW |
| 作者单位 | 1.CHINESE UNIV HONG KONG,DEPT MATH,SHATIN,HONG KONG 2.CHINESE ACAD SCI,INST APPL MATH,BEIJING,PEOPLES R CHINA |
| 推荐引用方式 GB/T 7714 | Sun, HW,Chan, RH,Chang, QS. A note on the convergence of the two-grid method for Toeplitz systems[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,1997,34(1):11-18. |
| APA | Sun, HW,Chan, RH,&Chang, QS.(1997).A note on the convergence of the two-grid method for Toeplitz systems.COMPUTERS & MATHEMATICS WITH APPLICATIONS,34(1),11-18. |
| MLA | Sun, HW,et al."A note on the convergence of the two-grid method for Toeplitz systems".COMPUTERS & MATHEMATICS WITH APPLICATIONS 34.1(1997):11-18. |
入库方式： OAI收割
来源：数学与系统科学研究院
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