A Novel Approach to the Shifted QR Algorithm for the Hermitian Eigenvalue Problem

Abstract

We present two novel algorithms for computing the eigenvectors of an Hermitian matrix. The algorithms are based on the shifted QR algorithm. We show how viewing the shifted QR algorithm in terms of subspace iteration and Rayleigh quotient iteration (RQI) can lead to algorithms which are more naturally suited to adaptive computation of the eigen-structure of Hermitian matrices than the standard algorithm. We also show the algorithms to be theoretically similar to each other.