Using this approach as a electromagnetic inverse scattering problems using nonlinear guide, we will seek to develop a more robust preconditioner conjugate gradient (NLCG) and limited memory (LM) quasi-using approximate data sensitivities based on the ideas of Newton methods. Key to our approach is the use of an Farquharson and Oldenburg (1996). At each inversion approximate adjoint method that allows for an economical iteration the idea is to more accurately estimate the data approximation of the Hessian that is updated at each inversion component of the Hessian so it can be applied as a iteration. Using this approximate Hessian as a preconditoner, preconditioner in both the nonlinear conjugate gradient we show that the preconditioned NLCG iteration converges (NLCG) and the limited memory (LM) quasi-Newton significantly faster than the non-preconditioned iteration, as schemes, where efficiency is paramount for 3D inverse well as converging to a data misfit level below that observed problems. These later schemes have the potential to perform for the non-preconditioned problem. Similar conclusions are even better than NLCG schemes. These methods can be seen also observed for the LM iteration; preconditioned with the as extensions of the conjugate gradient method, in which approximate Hessian, the LM iteration converges faster than additional storage is used to accelerate convergence.