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:在本篇文章中,我们概述了在非线性二次价值问题的背景下提出的各种事后错误分析和后处理方法,例如,在计算地面状态和比较时产生的电子结构计算方法;我们根据泰勒在第二顺序上扩大最小化能源或非线性二次价值方程上扩大第一顺序来进行两种等效错误的重新校正;我们然后说明如何将若干事后错误估计和后处理方法形成出自的重现错误的具体应用,并比较其适用性范围以及数字成本和精确度。</s>