A new gradient method with an optimal stepsize property
文献类型：期刊论文
| 作者 | Dai, YH ; Yang, XQ
|
| 刊名 | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
 |
| 出版日期 | 2006 |
| 卷号 | 33期号:1页码:73-88 |
| 关键词 | linear system gradient method steepest descent method (shifted) power method |
| ISSN号 | 0926-6003 |
| DOI | 10.1007/s10589-005-5959-2 |
| 英文摘要 | The gradient method for the symmetric positive definite linear system Ax = b is as follows x(k+1) = x(k) - alpha(k)g(k) where g(k) = Ax(k) - b is the residual of the system at x(k) and alpha(k) is the stepsize. The stepsize alpha(k) = 2/lambda(1)+lambda(n) is optimal in the sense that it minimizes the modulus parallel to I - alpha A parallel to(2), where.1 and.n are the minimal and maximal eigenvalues of A respectively. Since lambda(1) and lambda(n) are unknown to users, it is usual that the gradient method with the optimal stepsize is only mentioned in theory. In this paper, we will propose a new stepsize formula which tends to the optimal stepsize as k -> infinity. At the same time, the minimal and maximal eigenvalues,.1 and.n, of A and their corresponding eigenvectors can be obtained. |
| WOS研究方向 | Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000235317800004 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3678]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Dai, YH |
| 作者单位 | 1.Chinese Acad Sci, Acad Math& Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Dai, YH,Yang, XQ. A new gradient method with an optimal stepsize property[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2006,33(1):73-88. |
| APA | Dai, YH,&Yang, XQ.(2006).A new gradient method with an optimal stepsize property.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,33(1),73-88. |
| MLA | Dai, YH,et al."A new gradient method with an optimal stepsize property".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 33.1(2006):73-88. |
入库方式： OAI收割
来源：数学与系统科学研究院
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