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

Abstract

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.

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• Perspective on Moreau-Yosida Regularization in Density-Functional Theory
• Fully guaranteed and computable error bounds on the energy for periodic Kohn-Sham equations with convex density functionals