  In this paper we develop a convergence analysis in an infinite dimensional
setting of the Levenberg-Marquardt iteration for the solution of a hybrid
conductivity imaging problem. The problem consists in determining the spatially
varying conductivity $\sigma$ from a series of measurements of power densities
for various voltage inductions. Although this problem has been very well
studied in the literature, convergence and regularizing properties of iterative
algorithms in an infinite dimensional setting are still rudimentary. We provide
a partial result under the assumptions that the derivative of the operator,
mapping conductivities to power densities, is injective and the data is
noise-free. Moreover, we implemented the Levenberg-Marquardt algorithm and
tested it on simulated data.
