A New Convergent Algorithm to Approximate Potentials from Fixed Angle Scattering Data

Abstract

We introduce a new iterative method to recover a real compact supported potential of the Schödinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the resolvent of the Schödinger operator by partial sums associated to its Born series. The main interest is that, unlike other iterative methods in the literature, each iteration is explicit (and therefore faster computationally) and a rigorous analytical result on the convergence of the iterations is proved. This result requires potentials with small norm in certain Sobolev spaces. As an application we show some numerical experiments that illustrate this convergence.