A numerical method for solving 3D inverse scattering problem with non-over-determined data

A new numerical method is given for solving 3D inverse scattering problem (ISP) with non-over-determined scattering data. No such results were known. The ISP is not solved by a parameter fitting procedure. The method is based on the author’s uniqueness theorem. The data are the values of the scattering amplitude for all β∈S²β, where S²β is an open subset of the unit sphere S² in ℝ³, α₀ ∈ S² is fixed, and all k ∈ (a,b), where 0 ≤ a < b. The basic uniqueness theorem for solving the inverse scattering problem with non-over-determined scattering data belongs to the author. Earlier there were no results on numerical methods for solving the inverse scattering problem with such data. The proposed numerical method for solving the inverse scattering problem is original. It is based on the author’s uniqueness theorem and on his method for stable solution of ill-conditioned linear algebraic systems. Since the inverse scattering problem is non-linear, it is of prime interest that the basic step of the proposed inversion procedure consists of solving linear algebraic system.