Numerical approximation of the potential in the two-dimesional inverse scattering problem. (10th December 2015)

• Record Type: Journal Article
• Authors: Barceló, Juan A; Castro, Carlos; Reyes, Juan M
• Is Part Of: Inverse problems. Volume 32:Number 1(2016:Jan.)
• Publication Date: 2015-12-10
• Subjects: inverse scattering problem -- far field pattern -- Born approximation -- Lippmann–Schwinger equation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/1/015006
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We present an iterative algorithm to compute numerical approximations of the potential for the Schrödinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle, backscattering and full data. In the case of fixed energy, the algorithm coincides basically with the one recently introduced by Novikov (2015 Sbornik: Math. 206 120–34 ), where some estimates are obtained for large energy scattering data. The numerical results that we present here are consistent with these estimates.