  In this article, we present two new greedy algorithms for the computation of
the lowest eigenvalue (and an associated eigenvector) of a high-dimensional
eigenvalue problem, and prove some convergence results for these algorithms and
their orthogonalized versions. The performance of our algorithms is illustrated
on numerical test cases (including the computation of the buckling modes of a
microstructured plate), and compared with that of another greedy algorithm for
eigenvalue problems introduced by Ammar and Chinesta.
