Numerical results of solving 3D inverse scattering problem with non-over-determined data

We consider the 3D inverse scattering problem with non-over-determined scattering data. The data are the scattering amplitude $A(\beta ,{\alpha }_0,k)$ for all $\beta \in S_{\beta }^2$, where $S_{\beta }^2$ is an open subset of the unit sphere $S^2$ in ${\mathbb{R}}^3$, ${\alpha }_0\in S^2$ is fixed, and for all $k\in (a,b),0\le a<b$. The basic uniqueness theorem for this problem belongs to Ramm \cite{R603}. In this paper, a numerical method is given for solving this problem and the numerical results are presented.