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A potential-free field inverse Schrodinger problem: optimal error bound analysis and regularization method
Yang, Fan; Fu, Jun-Liang; Li, Xiao-Xiao
2019-12-14
Source PublicationINVERSE PROBLEMS IN SCIENCE AND ENGINEERING
ISSN1741-5977
AbstractIn this paper, an inverse Schrodinger problem of potential-free field is studied. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. Based on an a priori assumption, the optimal errorbound analysis is given. Moreover, two different regularization methods are used to solve this problem, respectively. Under an a priori and an a posteriori regularization parameters choice rule, the convergent error estimates are all obtained. Compared with Landweber iterative regularization method, the convergent estimate between the exact solution and the regularization solution obtained by a modified kernel method is optimal for the priori regularization parameter choice rule, and the posteriori error estimate is order-optimal. Finally, some numerical examples are given to illustrate the effectiveness, stability and superiority of these methods.
KeywordPotential-free field inverse Schrodinger problem optimal error bound Landweber iterative regularization method a modified kernel method ill-posed problem
DOI10.1080/17415977.2019.1700243
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11561045,11961044]
WOS Research AreaEngineering ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000503306400001
PublisherTAYLOR & FRANCIS LTD
Document Type期刊论文
Identifierhttp://ir.lut.edu.cn/handle/2XXMBERH/64280
Collection理学院
Corresponding AuthorYang, Fan
AffiliationLanzhou Univ Technol, Sch Sci, Lanzhou 730050, Gansu, Peoples R China
First Author AffilicationColl Sci
Corresponding Author AffilicationColl Sci
First Signature AffilicationColl Sci
Recommended Citation
GB/T 7714
Yang, Fan,Fu, Jun-Liang,Li, Xiao-Xiao. A potential-free field inverse Schrodinger problem: optimal error bound analysis and regularization method[J]. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING,2019.
APA Yang, Fan,Fu, Jun-Liang,&Li, Xiao-Xiao.(2019).A potential-free field inverse Schrodinger problem: optimal error bound analysis and regularization method.INVERSE PROBLEMS IN SCIENCE AND ENGINEERING.
MLA Yang, Fan,et al."A potential-free field inverse Schrodinger problem: optimal error bound analysis and regularization method".INVERSE PROBLEMS IN SCIENCE AND ENGINEERING (2019).
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