Record number :

1135524

Title of article :

Preconditioned conjugate gradient method for the sparse generalized eigenvalue problem in electronic structure calculations Original Research Article

Author/Authors :

C.K. Gan، نويسنده , , P.D. Haynes، نويسنده , , Susan M.C. Payne، نويسنده ,

Issue Information :

دوهفته نامه با شماره پیاپی سال 2001

Pages :

8

From page :

33

To page :

40

Abstract :

The use of localized basis sets is essential in linear-scaling electronic structure calculations, and since such basis sets are mostly non-orthogonal, it is necessary to solve the generalized eigenvalue problem Hx=εSx. In this work, an iterative method for finding the lowest few eigenvalues and corresponding eigenvectors for the generalized eigenvalue problem based on the conjugate gradient method is presented. The method is applied to first-principles electronic structure calculations within density-functional theory using a localized spherical-wave basis set, first introduced in the context of linear-scaling methods [Comput. Phys. Commun. 102 (1997) 17]. The method exhibits linear convergence of the solution, the rate of which is improved by a preconditioning scheme using the kinetic energy matrix.

Keywords :

Electronic structure , Preconditioning , Conjugate gradient , Eigenvalue problem

Journal title :

Computer Physics Communications

Serial Year :

2001

Link To Document :