2020/01/25 by Xiaoying Dai, Liwei Zhang, Dai, Xiaoying +3
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Chemical and Physical Properties of Materials #FOS: Mathematics #Force Microscopy Techniques and Applications #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.2001.09285
33 pages, 5 figures, 1 table
arxiv created 2020/01/25 · openalex publication_date 2020/01/25 · arxiv updated 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.