FEAST as a subspace iteration eigensolver accelerated by approximate spectral projection (Q2923348)

Solving matrix eigenvalue problems is crucial in many scientific and engineering applications. In many applications linear systems are large and sparse, it is often the case that only selected segments of the spectrum are of interest. The second author recently proposed a density-matrix-based algorithm named FEAST for Hermitian eigenproblems of this kind [The FEAST solver, \url{http://www.ecs.umass.edu/~polizzi/feast/}, 2009.]. A detailed numerical analysis of FEAST offered. The FEAST algorithm can be understood as standard subspace iteration in conjunction with the Rayleigh-Ritz procedure shown in this paper.