Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices
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.
quasi degenerate variational perturbation theory
scientific article; zbMATH DE number 149160