Fast diagonalisation of nonlocal pseudopotential Hamiltonians
Fast diagonalisation of nonlocal pseudopotential Hamiltonians
复制标题
非局部赝势哈密顿量的快速对角化
DOI：
10.1088/0953-8984/1/3/004
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
J. Michenaud
中科院分区：
文献类型：
--
作者：
X. Gonze;J. Vigneron;J. Michenaud
固体能带结构和总能量的计算涉及到寻找大矩阵（大小为N × N）的少数最低（M）本征向量和本征值。将矩阵对角化的标准算法完全按比例缩放为N3，而仅提取M个特征值和特征向量的子集的过程按比例缩放为MN 2。本文介绍了两种求非定域赝势哈密顿量的最低本征值和相应本征向量的方法。这两种方法都导致了一个算法，其规模大致为MN 4/3。
The calculation of band structure and total energy of solids involves the search for the few lowest (M) eigenvectors and eigenvalues of large matrices (size N × N). Standard algorithms which diagonalise the matrix entirely scale as N3, while procedures for extracting only a subset of M eigenvalues and eigenvectors scale as MN2. Two methods are described which aim at finding the lowest eigenvalues and corresponding eigenvectors of a nonlocal pseudopotential Hamiltonian. Both approaches lead to an algorithm which scales roughly as MN4/3.