On the separable nonlinear least squares problems

	On the separable nonlinear least squares problems
	Liu, Xin1,2 ; Yuan, Yaxiang1
	2008-05-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	26 期号:3 页码:390-403
摘要	Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.
关键词	separable nonlinear least squares problem variable projection method Gauss-Newton method Levenberg-Marquardt method trust region method asymptotical convergence rate data fitting
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000256648500011
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6125
专题	计算数学与科学工程计算研究所
通讯作者	Liu, Xin
作者单位	1.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Xin,Yuan, Yaxiang. On the separable nonlinear least squares problems[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2008,26(3):390-403.
APA	Liu, Xin,&Yuan, Yaxiang.(2008).On the separable nonlinear least squares problems.JOURNAL OF COMPUTATIONAL MATHEMATICS,26(3),390-403.
MLA	Liu, Xin,et al."On the separable nonlinear least squares problems".JOURNAL OF COMPUTATIONAL MATHEMATICS 26.3(2008):390-403.