  We consider an electron in a localized potential submitted to a weak
external, timedependent field. In the linear response regime, the response
function can be computed using Kubo's formula. In this paper, we consider the
numerical approximation of the response function by means of a truncation to a
finite region of space. This is necessarily a singular approximation because of
the discreteness of the spectrum of the truncated Hamiltonian, and in practice
a regularization (smoothing) has to be used. Our results provide error
estimates for the response function past the ionization threshold with respect
to both the smoothing parameter and the size of the computational domain.
