A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix
A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix
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DOI：
10.1016/0010-4655(94)90073-6
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发表时间：
1994-04
影响因子：
6.3
通讯作者：
A. Stathopoulos;C. Fischer
中科院分区：
文献类型：
--
作者：
A. Stathopoulos;C. Fischer
本文给出了一个计算大型真实的对称矩阵谱两端特征值及其特征向量的程序。基于在量子化学/物理学中广泛使用的Davidson方法，当前实现通过采用几个扩展来提高原始算法的能力。它需要的矩阵向量乘法例程由用户提供。因此，不同的矩阵格式和优化是可行的。一个有效的稀疏矩阵表示和矩阵向量乘法的例子。与Lanczos方法的比较表明了该程序的有效性。
A program is presented for determining a few selected eigenvalues and their eigenvectors on either end of the spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively used in quantum chemistry/physics, the current implementation improves the power of the original algorithm by adopting several extensions. The matrix-vector multiplication routine that it requires is to be provided by the user. Different matrix formats and optimizations are thus feasible. Examples of an efficient sparse matrix representation and a matrix-vector multiplication are given. Some comparisons with the Lanczos method demonstrate the efficiency of the program.