  We propose a new type of multilevel method for solving eigenvalue problems
based on Newton iteration. With the proposed iteration method, solving
eigenvalue problem on the finest finite element space is replaced by solving a
small scale eigenvalue problem in a coarse space and solving a series of
augmented linear problems, derived by Newton step in the corresponding series
of finite element spaces. This iteration scheme improves overall efficiency of
the finite element method for solving eigenvalue problems. Finally, some
numerical examples are provided to validate the efficiency of the proposed
numerical scheme.
