A potential-free field inverse Schrodinger problem: optimal error bound analysis and regularization method

doi:10.1080/17415977.2019.1700243

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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
发表期刊	INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
ISSN	1741-5977
卷号	28 期号:9 页码:1209-1252
摘要	In 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.
关键词	Potential-free field inverse Schrodinger problem optimal error bound Landweber iterative regularization method a modified kernel method ill-posed problem
DOI	10.1080/17415977.2019.1700243
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11561045,11961044]
WOS研究方向	Engineering ; Mathematics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000503306400001
出版者	TAYLOR & FRANCIS LTD
引用统计	被引频次：12[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://ir.lut.edu.cn/handle/2XXMBERH/64280
专题	理学院
通讯作者	Yang, Fan
作者单位	Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Gansu, Peoples R China
第一作者单位	理学院
通讯作者单位	理学院
第一作者的第一单位	理学院
推荐引用方式 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,2019,28(9):1209-1252.
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,28(9),1209-1252.
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 28.9(2019):1209-1252.