On the separable nonlinear least squares problems
文献类型：期刊论文
| 作者 | Liu, Xin1,2 ; Yuan, Yaxiang1
|
| 刊名 | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 2008-05-01 |
| 卷号 | 26期号:3页码:390-403 |
| 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 |
| ISSN号 | 0254-9409 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000256648500011 |
| 出版者 | GLOBAL SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6124]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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