Enhancing the Performance and Robustness of the FEAST Eigensolver

TL;DR

This paper proposes two methods to improve the convergence robustness of the FEAST eigensolver, especially in challenging cases with densely packed eigenvalues near the search interval edges, without increasing computational effort.

Contribution

The authors introduce two novel techniques that enhance FEAST's robustness against slow convergence in dense eigenvalue regions, maintaining efficiency.

Findings

Improved convergence in dense eigenvalue regions

Maintained computational efficiency

Numerical examples demonstrate effectiveness

Abstract

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