For a wide class of linear selfadjoint operators A on a Hilbert space the eigenvalues of the linear eigenvalue problem can be characterized by three fundamental variational principles, namely by Rayleigh’s principle, by Poincaré’s minmax characterization, and by the maxmin principle of Courant, Fischer and Weyl.
In this project we study corresponding characterizations for nonlinear egenproblems. They are applied in vibrations of fluid–solid structures, a priori bounds for automated multi–level structuring, locking strategies for iterative projection methods, and electronic structure calculation.