On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption

doi:10.1007/s00607-004-0083-1

	On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
	Fan, JY; Yuan, YX
	2005-02-01
发表期刊	COMPUTING
ISSN	0010-485X
卷号	74 期号:1 页码:23-39
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.
关键词	nonlinear equations Levenberg-Marquardt method quadratic convergence
DOI	10.1007/s00607-004-0083-1
语种	英语
WOS研究方向	Computer Science
WOS类目	Computer Science, Theory & Methods
WOS记录号	WOS:000226886500002
出版者	SPRINGER WIEN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1367
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.