Numerical approximation of the potential in the two-dimensional inverse scattering problem
This work provides a numerical implementation of a known iterative method for inverse scattering, offering validation but no new theoretical or practical breakthroughs.
The authors propose an iterative algorithm for numerically approximating the potential in the Schrödinger operator from scattering data, using four data types. Numerical results confirm theoretical estimates for large energy scattering data.
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 in [Novikov, R. G., "An iterative approach to non-overdetermined inverse scattering at fixed energy", Sbornik: Mathematics 206 (1), 120-134 (2015)], where some estimates are obtained for large energy scattering data. The numerical results that we present here are consistent with these estimates.