A Mixed Regularization Method for Ill-Posed Problems

doi:10.4208/nmtma.OA-2017-0079

	A Mixed Regularization Method for Ill-Posed Problems
	Zheng, Hui 1,2; Zhang, Wensheng2,3
	2019-02-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	12 期号:1 页码:212-232
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.
关键词	Ill-posedness continuous regularization iterative regularization mixed regularization optimal order
DOI	10.4208/nmtma.OA-2017-0079
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000444827500010
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/31238
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.