Enhancing the performance and robustness of the FEAST eigensolver

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.