  The computation of eigenvalues of large-scale matrices arising from finite
element discretizations has gained significant interest in the last decade.
Here we present a new algorithm based on slicing the spectrum that takes
advantage of the rank structure of resolvent matrices in order to compute m
eigenvalues of the generalized symmetric eigenvalue problem in $\mathcal{O}(n m
\log^\alpha n)$ operations, where $\alpha>0$ is a small constant.
