The investigation of the full eigenvalue and eigenvector problem in the case of multiple or close eigenvalues taking into account the discrepancy in initial data, brings about a generation of new algorithms. These algorithms amount to minimizing convex functionals and are of particular assistance in the case of highly dimensional problems. The understanding of the geometrical meaning of various stabilizing functionals makes it possible to use apriori information about eigenvectors corresponding to multiple eigenvalues. For instance, by this expedient it is possible to fix the directions of such eigenvectors. © 2001 IOS Press.