Improving robustness of the FEAST algorithm and solving eigenvalue problems from graphene nanoribbons

The FEAST algorithm [5] is an algorithm aimed at solving generalized eigenvalue problems AX = BXΛ, where A,B are n×n matrices. In [4] we presented a short analysis of FEAST involving this eigenvalue problem. In the present work we focus on the real symmetric eigenvalue problem AX = XΛ, where A = A, XX = I and Λ is a diagonal matrix consisting of real eigenvalues. These eigenvalues are sought in a given interval Iλ = [λ, λ]. The FEAST method aims at solving this particular eigenvalue problem by performing Rayleigh–Ritz [6]. The involved subspace is spanned by