On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
文献类型：期刊论文
| 作者 | Fan, JY; Yuan, YX
|
| 刊名 | COMPUTING
 |
| 出版日期 | 2005-02-01 |
| 卷号 | 74期号:1页码:23-39 |
| 关键词 | nonlinear equations Levenberg-Marquardt method quadratic convergence |
| ISSN号 | 0010-485X |
| DOI | 10.1007/s00607-004-0083-1 |
| 英文摘要 | Recently, Yamashita and Fukushima [11] established an interesting quadratic convergence result for the Levenberg-Marquardt method without the nonsingularity assumption. This paper extends the result of Yamashita and Fukushima by using mu(k)=parallel toF(x(k))parallel to(delta) where delta is an element of [1,2], instead of mu(k)=parallel toF(x(k))parallel to(2) as the Levenberg-Marquardt parameter. If parallel toF(x)parallel to provides a local error bound for the system of nonlinear equations F(x)=0, it is shown that the sequence {x(k)} generated by the new method converges to a solution quadratically, which is stronger than dist(x(k),X*) --> 0 given by Yamashita and Fukushima. Numerical results show that the method performs well for singular problems. |
| WOS研究方向 | Computer Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000226886500002 |
| 出版者 | SPRINGER WIEN |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1366]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Fan, JY |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Fan, JY,Yuan, YX. On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption[J]. COMPUTING,2005,74(1):23-39. |
| APA | Fan, JY,&Yuan, YX.(2005).On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption.COMPUTING,74(1),23-39. |
| MLA | Fan, JY,et al."On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption".COMPUTING 74.1(2005):23-39. |
入库方式： OAI收割
来源：数学与系统科学研究院
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