The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM, and the closely-related multiple Bennett acceptance ratio method can be improved using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

中文翻译：

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在迭代子空间中通过直接反演加速加权直方图分析方法

用于自由能计算的加权直方图分析方法 (WHAM) 是一种有价值的工具，可以以最小的误差产生自由能差异。给定多次模拟，WHAM 从分布中获得重叠状态密度的最佳统计估计量，从中可以计算出自由能差异。WHAM 方程通常通过迭代程序求解。在这项工作中，我们使用了一个众所周知的线性代数算法，它允许更快地收敛到解决方案。我们发现在迭代子空间中使用直接反演的方法可以提高WHAM迭代解的计算复杂度，以及密切相关的多重贝内特接受率方法。我们给出了晶格模型、简单液体和蛋白质水溶液的例子。