论文标题
电子结构计算的牛顿法典方法
Pactical Newton Methods for Electronic Structure Calculations
论文作者
论文摘要
在本文中，我们提出和分析了一些用于电子结构计算的牛顿方法。当牛顿搜索方向良好时，我们显示了牛顿方法的收敛和局部二次收敛率。特别是，我们研究了确定搜索方向和步进大小的一些基本实现问题，这些问题可确保在每次迭代中分别加速算法在每次迭代中的收敛性。我们的数值实验表明，我们的牛顿方法的性能优于现有的共轭梯度方法，而具有自适应步长策略的牛顿方法更有效。
In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the Newton method when the Newton search directions are well-obtained. In particular, we investigate some basic implementation issues in determining the search directions and step sizes which ensures the convergence of the subproblem at each iteration and accelerates the algorithm, respectively. It is shown by our numerical experiments that our Newton methods perform better than the existing conjugate gradient method, and the Newton method with the adaptive step size strategy is even more efficient.
