  In this paper we consider a reduced order method for the approximation of the
eigensolutions of the Laplace problem with Dirichlet boundary condition. We use
a time continuation technique that consists in the introduction of a fictitious
time parameter. We use a POD approach and we present some theoretical results
showing how to choose the optimal dimension of the POD basis. The results of
our computations, related to the first eigenvalue, confirm the optimal behavior
of our approximate solution.
