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

References in corpus (2)

• H-matrix approximability of the inverses of FEM matrices
• Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates

Cited by in corpus (1)

• Computing the k-th Eigenvalue of Symmetric $H^2$-Matrices