A potential-free field inverse Schrödinger problem: optimal error bound analysis and regularization method. Issue 9 (1st September 2020)

• Record Type: Journal Article
• Authors: Yang, Fan; Fu, Jun-Liang; Li, Xiao-Xiao
• Is Part Of: Inverse problems in science and engineering. Volume 28:Issue 9(2020)
• Page Start: 1209
• Page End: 1252
• Publication Date: 2020-09-01
• Subjects: Potential-free field inverse Schrödinger problem -- optimal error bound -- Landweber iterative regularization method -- a modified kernel method -- ill-posed problem; 65M32 -- 35R11; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2019.1700243
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : In this paper, an inverse Schrödinger 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.