  A cascadic multigrid method is proposed for eigenvalue problems based on the
multilevel correction scheme. With this new scheme, an eigenvalue problem on
the finest space can be solved by smoothing steps on a series of multilevel
finite element spaces and eigenvalue problem solving on the coarsest finite
element space. Choosing the appropriate sequence of finite element spaces and
the number of smoothing steps, the optimal convergence rate with the optimal
computational work can be arrived. Some numerical experiments are presented to
validate our theoretical analysis.
