Acta Phys. -Chim. Sin. ›› 2008, Vol. 24 ›› Issue (05): 823-826.doi: 10.3866/PKU.WHXB20080515

• ARTICLE • Previous Articles     Next Articles

Iterative Calculations of a Few Lowest Eigenvalues and Corresponding Eigenvectors of Large Generalized Eigenvalue Problem

ZHAO Xiao-Hong; CHEN Fei-Wu; WU Jian; ZHOU Qiao-Long   

  1. Department of Chemistry, University of Science and Technology Beijing, Beijing 100083, P. R. China
  • Received:2007-11-22 Revised:2008-02-28 Published:2008-05-05
  • Contact: CHEN Fei-Wu E-mail:chenfeiwu@sas.ustb.edu.cn

Abstract: We extended the Davidson method, which was used to solve the standard eigenvalue problem, to solve the generalized eigenvalue problem and proposed the corresponding block iterative algorithm. Through theoretical analysis and numerical calculation, we found that the block iterative algorithm was doomed to converge after finite iterations if the process of iteration was not divergent. If the dimension of the matrix is n, the number of the eigenvalues and corresponding eigenvectors to be calculated is k, the size of the initial subspace is r(r≥k), the number of iteration is m, then they will fit in with the equation n=r+km. The positive integer root m could be obtained by regulating the size of the subspace.

Key words: Generalized eigenvalue problem, Eigenvalue, Eigenvector

MSC2000: 

  • O641