Convergence rate analysis of a derivative free landweber iteration for parameter identification in certain elliptic PDEs

We consider the nonlinear inverse problem of identifying a parameter from knowledge of the physical state in an elliptic partial differential equation. For a derivative free Landweber method, convergence rates are proven under a weak source condition not involving the standard Frechet derivative of the nonlinear parameter-to-output map. This source condition is discussed both for the estimation of state- and space-dependent parameters in higher dimensions. Finally, numerical results are presented.