论文标题
线性缩放电子结构计算的不完整反转倒置
Incomplete selected inversion for linear-scaling electronic structure calculations
论文作者
论文摘要
极点膨胀和选定的反转（PEXSI）是一种有效的方案，用于评估所需的大稀疏矩阵功能的条目，例如在电子结构算法中。我们表明，由PEXSI方案计算的三角因素化具有与矩阵函数相似的定位属性，并且我们提出了一种修改的PEXSI算法，该算法利用了该观察值以实现线性缩放。 To the best of our knowledge, the resulting incomplete PEXSI (iPEXSI) algorithm is the first linear-scaling algorithm which scales provably better than cubically even in the absence of localization, and we hope that this will help to further lower the critical system size where linear-scaling algorithms begin to outperform the diagonalization algorithm.
Pole Expansion and Selected Inversion (PEXSI) is an efficient scheme for evaluating selected entries of functions of large sparse matrices as required e.g. in electronic structure algorithms. We show that the triangular factorizations computed by the PEXSI scheme exhibit a localization property similar to that of matrix functions, and we present a modified PEXSI algorithm which exploits this observation to achieve linear scaling. To the best of our knowledge, the resulting incomplete PEXSI (iPEXSI) algorithm is the first linear-scaling algorithm which scales provably better than cubically even in the absence of localization, and we hope that this will help to further lower the critical system size where linear-scaling algorithms begin to outperform the diagonalization algorithm.
