Virginie Ehrlacher École Nationale des Ponts-et-Chaussées CERMICS Greedy algorithms are promising algorithms to treat high-dimensional PDEs. Encouraging numerical results have already been obtained in a large number of applications. Until recently, theoretical convergence results have only been obtained for nonlinear convex optimization problems. The aim of this talk is to present new convergence results for this family of numerical methods regarding high-dimensional eigenvalue linear problems. We will illustrate the numerical behavior of these algorithms on a simple test case: the computation of the first buckling mode of cellular materials in the presence of defects.