  We present a general setting in which the formula describing the linear
response of the physical measure of a perturbed system can be obtained. In this
general setting we obtain an algorithm to rigorously compute the linear
response. We apply our results to expanding circle maps. In particular, we
present examples where we compute, up to a pre-specified error in the
$L^{\infty}$-norm, the response of expanding circle maps under stochastic and
deterministic perturbations. Moreover, we present an example where we compute,
up to a pre-specified error in the $L^1$-norm, the response of the intermittent
family at the boundary; i.e., when the unperturbed system is the doubling map.
