Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum

Abstract

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 $\mathcal{O}(n m \log^αn)$ operations, where $α>0$ is a small constant.