Minimization Principles for the Linear Response Eigenvalue Problem II: Computation

In Part I of this paper we presented minimization principles and related theoretical results for the linear response eigenvalue problem. Here we develop best approximations for the few smallest eigenvalues with the positive sign via a structure-preserving subspace projection. Then we present four-dimensional subspace search conjugate gradient-like algorithms for simultaneously computing these eigenvalues and their associated eigenvectors. Finally, we present numerical examples to illustrate convergence behaviors of the proposed methods with and without preconditioning.