Least-squares Rational Filters for the Solution of Interior Eigenvalue Problems

This paper presents a method for computing partial spectra of Hermitian matrices, based on a subspace iteration method combined with rational filtering. While the general approach is the same as that of the FEAST package, the emphasis of this paper is on the selection of the filter. Specifically, the goal is to show the appeal of a least-squares viewpoint for designing filters. In particular, the paper shows how to define filters with repeated poles and demonstrates that this option can be attractive when iterative methods are used.