The reactivity computations are an essential component for the simulation of the core of a nuclear plant. These computations lead to generalized eigenvalue problems solved by the inverse power iteration algorithm. At each iteration, an algebraic linear system is solved through an inner/outer process. With the solver Cocagne developed at EDF, it is difficult to take into account very fine discretisation, due to the memory requirement and the computation time. In this thesis, a domain decomposition method based on the Schur dual technique is studied. Several placements in the inner/outer process are possible. Two of them are implemented and the results analyzed. The second one, which uses the specificities of the Raviart Thomas finite elements and of the alternating directions algorithm, leads to very promising results. From these results the industrialization of the method can be considered.