A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix

Abstract
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. E...

Title of program: DVDSON
Catalogue Id: ACPZ_v1_0

Nature of problem
Finding a few extreme eigenpairs of a real, symmetric matrix is of great importance in scientific computations. Examples abound in structural engineering, quantum chemistry and electronic structure physics [1,2]. The matrices involved are usually too large to be efficiently solved using standard methods. Moreover, their large size often prohibits full storage forcing various sparse representations. Even sparse representations cannot always be stored in main memory [3]. Thus, an iterative method ...

Versions of this program held in the CPC repository in Mendeley Data
ACPZ_v1_0; DVDSON; 10.1016/0010-4655(94)90073-6

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本文介绍一款程序，可用于求解大型实对称矩阵谱两端的若干指定本征值（eigenvalue）及其本征向量（eigenvector）。该程序基于在量子化学/物理学中广泛应用的戴维森方法（Davidson method），通过引入多项扩展改进了原始算法的性能。程序所需的矩阵-向量乘法子程序需由用户自行提供，因此可适配不同的矩阵格式并进行优化。[原文后续内容省略]

程序名称：DVDSON
目录编号：ACPZ_v1_0

问题属性
求解实对称矩阵的少量极端本征对（eigenpair）在科学计算中具有重要意义。这类应用在结构工程、量子化学与电子结构物理学中比比皆是[1,2]。所涉及的矩阵通常规模过大，无法通过标准方法高效求解。此外，矩阵的超大尺寸往往导致无法完整存储，因此需要采用各类稀疏表示方式。即便采用稀疏表示，也未必能完全载入主存[3]。因此，迭代方法[原文后续内容省略]

本程序收录于Mendeley数据的CPC（Computer Physics Communications）程序库中，版本信息：ACPZ_v1_0；程序名称：DVDSON；引用标识：10.1016/0010-4655(94)90073-6

本程序源自贝尔法斯特女王大学所维护的CPC程序库（1969-2019年）