RECONSTRUCTING POTENTIALS FROM ZEROS OF ONE EIGENFUNCTION

被引：28

作者：

Chen, Xinfu ^{[1
]}

Cheng, Y. H. ^{[2
]}

Law, C. K. ^{[2
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 363卷 / 09期

基金：

美国国家科学基金会;

关键词：

Inverse nodal problem; Sturm-Liouville operators; Tikhonov regularization; error bound; INVERSE NODAL PROBLEM;

D O I：

10.1090/S0002-9947-2011-05258-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study an inverse nodal problem, concerning the reconstruction of a potential of a Sturm-Liouville operator, by using zeros of one eigenfunction as input. We propose three methods for the reconstruction, one of which is the Tikhonov regularization method. The explicit error bounds are calculated for all three methods. In case there is measurement error, the Tikhonov regularization method is still convergent. The study is motivated by physical considerations.

引用

页码：4831 / 4851

页数：21

共 15 条

[1]

[Anonymous], 1996, INTRO MATH THEORY IN

[2] OPTIMAL BOUNDS FOR RATIOS OF EIGENVALUES OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS WITH DIRICHLET BOUNDARY-CONDITIONS AND POSITIVE POTENTIALS [J].