Convergence of the multigrid method for ill-conditioned block Toeplitz systems
文献类型：期刊论文
| 作者 | Sun, HW; Jin, XQ; Chang, QS |
| 刊名 | BIT NUMERICAL MATHEMATICS
 |
| 出版日期 | 2001 |
| 卷号 | 41期号:1页码:179-190 |
| 关键词 | multigrid method block Toeplitz matrix |
| ISSN号 | 0006-3835 |
| 英文摘要 | We study the solutions of block Toeplitz systems A(mn)u = b by the multigrid method (MGM). Here the block Toeplitz matrices A(mn) are generated by a nonnegative function f(x; y) with zeros. Since the matrices A(mn) are ill-conditioned, the convergence factor of classical iterative methods will approach 1 as the size of the matrices becomes large. These classical methods, therefore, are not applicable for solving ill-conditioned systems. The MGM is then proposed in this paper. For a class of block Toeplitz matrices, we show that the convergence factor of the two-grid method (TGM) is uniformly bounded below 1 independent of mn and the full MGM has convergence factor depending only on the number of levels. The cost per iteration for the MGM is of O(mn log mn) operations. Numerical results are given to explain the convergence rate. |
| WOS研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000167334800010 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/16385]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 作者单位 | 1.Guangdong Univ Technol, Dept Math & Phys, Guangzhou 510090, Peoples R China 2.Univ Macau, Fac Sci & Technol, Macao, Peoples R China 3.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Sun, HW,Jin, XQ,Chang, QS. Convergence of the multigrid method for ill-conditioned block Toeplitz systems[J]. BIT NUMERICAL MATHEMATICS,2001,41(1):179-190. |
| APA | Sun, HW,Jin, XQ,&Chang, QS.(2001).Convergence of the multigrid method for ill-conditioned block Toeplitz systems.BIT NUMERICAL MATHEMATICS,41(1),179-190. |
| MLA | Sun, HW,et al."Convergence of the multigrid method for ill-conditioned block Toeplitz systems".BIT NUMERICAL MATHEMATICS 41.1(2001):179-190. |
入库方式： OAI收割
来源：数学与系统科学研究院
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