Multigrid method for ill-conditioned symmetric Toeplitz systems
文献类型：期刊论文
| 作者 | Chan, RH; Chang, QS; Sun, HW |
| 刊名 | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| 出版日期 | 1998-03-01 |
| 卷号 | 19期号:2页码:516-529 |
| 关键词 | multigrid method Toeplitz matrices |
| ISSN号 | 1064-8275 |
| 英文摘要 | In this paper, we consider solutions of Toeplitz systems A(n)u = b where the Toeplitz matrices A(n) are generated by nonnegative functions with zeros. Since the matrices A(n) are ill conditioned, the convergence factor of classical iterative methods, such as the damped Jacobi method, will approach one as the size n of the matrices becomes large. Here we propose to solve the systems by the multigrid method. The cost per iteration for the method is of O(n log n) operations. For a class of Toeplitz matrices which includes weakly diagonally dominant Toeplitz matrices, we show that the convergence factor of the two-grid method is uniformly bounded below one independent of n, and the full multigrid method has convergence factor depending only on the number of levels. Numerical results are given to illustrate the rate of convergence. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000071988000011 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13901]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Chan, RH |
| 作者单位 | 1.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong 2.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Chan, RH,Chang, QS,Sun, HW. Multigrid method for ill-conditioned symmetric Toeplitz systems[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,1998,19(2):516-529. |
| APA | Chan, RH,Chang, QS,&Sun, HW.(1998).Multigrid method for ill-conditioned symmetric Toeplitz systems.SIAM JOURNAL ON SCIENTIFIC COMPUTING,19(2),516-529. |
| MLA | Chan, RH,et al."Multigrid method for ill-conditioned symmetric Toeplitz systems".SIAM JOURNAL ON SCIENTIFIC COMPUTING 19.2(1998):516-529. |
入库方式： OAI收割
来源：数学与系统科学研究院
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