  We consider the problem of the recovery of a Robin coefficient on a part
$\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$
from the principal eigenvalue and the boundary values of the normal derivative
of the principal eigenfunction of the Laplace operator with Dirichlet boundary
condition on $\partial \Omega \setminus \gamma$. We prove uniqueness, as well
as local Lipschitz stability of the inverse problem. Moreover, we present an
iterative reconstruction algorithm with numerical computations in two
dimensions showing the accuracy of the method.
