  The FEAST algorithm is a subspace iteration method that uses a spectral
projector as a rational filter in order to efficiently solve interior
eigenvalue problems in parallel. Although the solutions from the FEAST
algorithm converge rapidly in many cases, convergence can be slow in situations
where the eigenvalues of a matrix are densely populated near the edges of the
search interval of interest, which can be detrimental to parallel load
balancing. This work introduces two methods that allow one to improve the
convergence robustness of the FEAST algorithm in these situations without
having to increase the amount of computation. Selected numerical examples are
presented and discussed
