The reconstruction in the Calderon inverse conductivity problem is considered. A suitable linearization of the inverse problem allows us to define the so-called Born approximation. This provides a good reconstruction only for the high frequencies of the conductivity. In a recent work, we established a new formula relating this Born approximation with the Dirichlet to Neumann map and the momenta of the conductivity coefficient. Based on this formula, we give a new convergent iterative algorithm that improves the numerical reconstruction given by the Born approximation. We illustrate the process with numerical experiments for radial and non-radial potentials.

 This is part of a collaboration work with J.A. Barceló, F. Macià, D. Mendoza,  and C. Meroño.