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.

翻译：本文综述了针对非线性特征值问题（如电子结构计算中基态计算相关场景）提出的多种后验误差分析与后处理方法，并对它们进行了比较。我们提供了两种等价的误差重构方法：一种基于最小化能量的二阶泰勒展开，另一种基于非线性特征值方程的一阶展开。进而展示了多种后验误差估计及后处理方法如何作为所导出重构误差的具体应用进行表述，并对它们的适用范围、数值计算成本及精度进行了比较。