We consider the scattering of time-harmonic electromagnetic
waves in inhomogeneous media.
The problem is to recover the electric permittivity
and conductivity of the medium from measurements of
scattered fields corresponding to incident fields
from all directions.
We first discuss the efficient numerical solution of
the direct scattering problem by a modification of Vainikko's
method, and provide an error analysis of this method.
Due to the large scale of the inverse problem, it
is not possible to use standard regularization methods.
Therefore, we propose new iterative methods which allow
the solution of the inverse problem with reasonable
computation time and storage requirements.
Moreover, we present a logarithmic stability estimate
where the data are measured in the L^2 norm.
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