Computing the eigenvalues of symmetric H2-matrices by slicing the   spectrum
  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. 
Peter Benner, Steffen B\"orm, Thomas Mach and Knut Reimer
math.NA