A Mixed Regularization Method for Ill-Posed Problems
文献类型：期刊论文
| 作者 | Zheng, Hui1,2; Zhang, Wensheng2,3
|
| 刊名 | NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
 |
| 出版日期 | 2019-02-01 |
| 卷号 | 12期号:1页码:212-232 |
| 关键词 | Ill-posedness continuous regularization iterative regularization mixed regularization optimal order |
| ISSN号 | 1004-8979 |
| DOI | 10.4208/nmtma.OA-2017-0079 |
| 英文摘要 | In this paper we propose a mixed regularization method for ill-posed problems. This method combines iterative regularization methods and continuous regularization methods effectively. First it applies iterative regularization methods in which there is no continuous regularization parameter to solve the normal equation of the ill-posed problem. Then continuous regularization methods are applied to solve its residual problem. The presented mixed regularization algorithm is a general framework. Any iterative regularization method and continuous regularization method can be combined together to construct a mixed regularization method. Our theoretical analysis shows that the new mixed regularization method is with optimal order of error estimation and can reach the optimal order under a much wider range of the regularization parameter than the continuous regularization method such as Tikhobov regularization. Moreover, the new mixed regularization method can reduce the sensitivity of the regularization parameter and improve the solution of continuous regularization methods or iterative regularization methods. This advantage is helpful when the optimal regularization parameter is hard to choose. The numerical computations illustrate the effectiveness of our new mixed regularization method. |
| 资助项目 | National Natural Science Foundation of China[11471328] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000444827500010 |
| 出版者 | GLOBAL SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/31237]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Zhang, Wensheng |
| 作者单位 | 1.Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zheng, Hui,Zhang, Wensheng. A Mixed Regularization Method for Ill-Posed Problems[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2019,12(1):212-232. |
| APA | Zheng, Hui,&Zhang, Wensheng.(2019).A Mixed Regularization Method for Ill-Posed Problems.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,12(1),212-232. |
| MLA | Zheng, Hui,et al."A Mixed Regularization Method for Ill-Posed Problems".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 12.1(2019):212-232. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。