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In this paper we develop a convergence analysis in an infinite dimensionalsetting of the Levenberg-Marquardt iteration for the solution of a hybridconductivity imaging problem. The problem consists in determining the spatiallyvarying conductivity $\sigma$ from a series of measurements of power densitiesfor various voltage inductions. Although this problem has been very wellstudied in the literature, convergence and regularizing properties of iterativealgorithms in an infinite dimensional setting are still rudimentary. We providea partial result under the assumptions that the derivative of the operator,mapping conductivities to power densities, is injective and the data isnoise-free. Moreover, we implemented the Levenberg-Marquardt algorithm andtested it on simulated data.

The Levenberg-Marquardt Iteration for Numerical Inversion of the Power Density Operator