The Iterative Calculation of Several of the Lowest or Highest Eigenvalues and Corresponding Eigenvectors of Very Large Symmetric Matrices
Abstract
The coordinate relaxation method for the iterative calculation of the lowest (or highest) root of a symmetric matrix, based on the minimization (or maximization) of the Rayleigh quotient, has been generalized to make it possible to obtain several of the lowest (or highest) roots in order without explicitly modifying the original matrix. The method is particularly suitable for very large matrices (even of order 104 or more), especially if they are sparse, such as those which occur in largescale configuration interaction calculations. A modified δ^{2} extrapolation procedure has been found to accelerate convergence in the more difficult cases, such as those involving nearly degenerate roots.
 Publication:

Journal of Computational Physics
 Pub Date:
 January 1973
 DOI:
 10.1016/00219991(73)901496
 Bibcode:
 1973JCoPh..11...90S