On reduced basis methods for eigenvalue problems, with an application to eigenvector continuation

Abstract

We provide inequalities enabling to bound the error between the exact solution and an approximated solution of an eigenvalue problem, obtained by subspace projection, as in the reduced basis method. We treat self-adjoint operators and degenerate cases. We apply the bounds to the eigenvector continuation method, which consists in creating the reduced space by using basis vectors extracted from perturbation theory.