Series reversion in Calderón’s problem

This work derives explicit series reversions for the solution of Calder\'on's problem. The governing elliptic partial differential equation is $\nabla\cdot(A\nabla u)=0$ in a bounded Lipschitz domain and with matrix-valued coefficient. corresponding forward map sends $A$ to projected version local Neumann-to-Dirichlet operator, allowing use boundary data finitely many measurements. It first shown that analytic, subsequently its Taylor up specified orders lead family numerical methods solving inverse problem increasing accuracy. convergence these under conditions ensure invertibility Fr\'echet derivative map. introduced are same computational complexity as linearised analogous results also presented smoothened complete electrode model.