Computing the eigenvalues of symmetric H 2-matrices by slicing the spectrum ∗

The computation of eigenvalues of large-scale matrices arising from finite ele-ment discretizations has gained significant interest in the last decade [18]. 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 gen-eralized symmetric eigenvalue problem in O(nm logα n) operations, where α> 0 is a small constant.