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

Published: 01-01-1994| Version 1 | DOI: 10.17632/tss3rwyynt.1
Andreas Stathopoulos,
Charlotte F. Fischer


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)