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：本程序旨在确定大型实对称矩阵两端的一组选定特征值及其特征向量。该程序基于在量子化学/物理学中广泛应用的Davidson方法，通过采纳数种扩展，增强了原始算法的效能。该程序所需的矩阵-向量乘法例程需由用户提供，因此不同矩阵格式和优化策略得以实现。...

程序名称：DVDSON
目录编号：ACPZ_v1_0

问题性质：在科学计算中，寻找实对称矩阵的若干极值特征对具有重要意义。在结构工程、量子化学和电子结构物理学等领域[1,2]中，此类例子比比皆是。涉及的矩阵通常规模庞大，难以使用标准方法高效求解。此外，其庞大规模往往导致无法完整存储，迫使采用各种稀疏表示。即便稀疏表示，也未必总能存储在主存中[3]。因此，一种迭代方法...

Mendeley数据中CPC存储库中保存的此程序版本：ACPZ_v1_0; DVDSON; 10.1016/0010-4655(94)90073-6

本程序已从贝尔法斯特女王大学（1969-2019）所持有的CPC程序库中导入。