Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum
This provides a faster method for eigenvalue computation in large-scale finite element problems, though it is incremental over existing spectral slicing techniques.
The authors present a new algorithm for computing eigenvalues of large symmetric matrices from finite element discretizations, achieving O(n m log^α n) complexity for m eigenvalues.
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.