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