We analyze the Funaro-Quarteroni alternative procedure for the solution of singular perturbation problems. We show that for an appropriate choice of the domain decomposition, one obtains a fast convergent iterative scheme with {\it no relaxation} that resolves the boundary layers. The convergence is superlinear with respect to the singular perturbation parameter $\epsilon$ in the following sense: the amplification factor is $o(\epsilon)$. We give sharp estimates of the interface position and convergent rates for an homogeneous domain decomposition in one dimensional space as well as in two dimensional space problems on a disk. We extend our results to heterogeneous domain decomposition arising in a simplified model of an electromagnetic problem. We report on implementation results with finite difference approximations and finite element codes ({\it Modulef})
