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Name:

Miloslav Znojil

Reviewer number:

9689

Email:

znojil@ujf.cas.cz

Item's zbl-Number:

DE016061301

Author(s):

Gan, C. K.; Haynes, P. D.; Payne, M. C.:

Shorttitle:

Preconditioned conjugate gradient method for the sparse generalized eigenvalue problem

Source:

Comput. Phys. Commun. 134, No. 1, 33-40 (2001).

Classification:

65F15

Eigenvalues, eigenvectors

Primary Classification:

Secondary Classification:

Keywords:

conjugate gradient method; generalized eigenvalue problem; preconditioning; the first few lowest eigensolutions;, application to electronic structure; chlorine molecule; silicon crystal; density functional approach; localised basis set

Review:

Paper inspired by the needs of solid state physics (the lowest few
energies and wave functions of the chlorine molecule and of a
64-atomic silicon crystal are calculated for illustration). Its
physical background is the density-functional theory represented
in localized (non-orthogonal) basis. The algorithm offered is an
iterative one, making an ample use of the sparsity of the matrices
in question (first of all, via a one-parametric family of the
kinetic-energy preconditionings). Empirically, the convergence
appears to be linear.

Remarks to the editors:

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