Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices
type: Item
instance of: scholarly article
title: Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices
zbMATH Open document ID: 0766.65037
DOI: 10.1016/0021-9991(92)90409-R
author: Christopher W. Murray
author: Stephen C. Racine
author: Ernest R. Davidson
published in: Journal of Computational Physics
publication date: 1993-04-01T00:00:00Z
review text: The configuration interaction method is used to calculate electronic wavefunctions for the ground state and excited states of atoms and molecules. It leads to the formation of a large, real, symmetric matrix for which the lowest eigenvalues and associated eigenvectors must be found. The Davidson algorithm is the most widely used approach for matrices of this type. A number of improvements to the usual implementation of that algorithm are discussed and some results are presented. The quasi degenerate variational perturbation theory, which is an alternative method for calculating electronic wavefunctions, is also considered. The similarities and differences between this approach and the Davidson algorithm are discussed. Some results that compare the performance of the two algorithms for similar matrices are given.
reviewed by: Zbigniew Dżygadło
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 149160
zbMATH Keywords: configuration interaction method
zbMATH Keywords: electronic wavefunctions
zbMATH Keywords: large, real, symmetric matrix
zbMATH Keywords: lowest eigenvalues
zbMATH Keywords: eigenvectors
zbMATH Keywords: Davidson algorithm
zbMATH Keywords: quasi degenerate variational perturbation theory
zbMATH Keywords: performance
MaRDI profile type: Publication
cites work: Generalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices
cites work: Conjugate gradient method for the solution of linear equations: Application to molecular electronic structure calculations
cites work: Calculation of eigenvectors of large matrices
cites work: A new method for diagonalising large matrices
description: scientific article; zbMATH DE number 149160