An overview of a posteriori error estimation and post-processing methods for nonlinear eigenvalue problems

Abstract

In this article, we present an overview of different a posteriori error analysis and post-processing methods proposed in the context of nonlinear eigenvalue problems, e.g. arising in electronic structure calculations for the calculation of the ground state and compare them. We provide two equivalent error reconstructions based either on a second-order Taylor expansion of the minimized energy, or a first-order expansion of the nonlinear eigenvalue equation. We then show how several a posteriori error estimations as well as post-processing methods can be formulated as specific applications of the derived reconstructed errors, and we compare their range of applicability as well as numerical cost and precision.