The inverse problem of identifying a certain coefficient function that appears in
an elliptic pde from (partial) knowledge of the physical state can be formulated
as a nonlinear operator equation. Standard iterative regularization routines for
solving the problem in a stable way pose severe restrictions on this nonlinear operator
and its Frechet-derivative. We present a derivative free iterative approach for which
convergence is obtained under natural assumptions. Taking an example from electrostatics,
we discuss the identification of an electrical conductivity that nonlinearily depends on
the magnitude of the electrical field.
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