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A Mixed Regularization Method for Ill-Posed Problems
Zheng, Hui1,2; Zhang, Wensheng2,3
AbstractIn 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.
KeywordIll-posedness continuous regularization iterative regularization mixed regularization optimal order
Funding ProjectNational Natural Science Foundation of China[11471328] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000444827500010
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Document Type期刊论文
Corresponding AuthorZhang, Wensheng
Affiliation1.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
Recommended Citation
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.
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