Computing interior eigenstates of large Hermitean matrices using a Richardson-Leja-Davidson scheme, with application to chemical physics

Hans Karlsson
Division of Quantum Chemistry
Department of Physical and Analytical Chemistry
Uppsala University


Abstract:

An efficient computational scheme for calculating interior eigenstates of very large Hermitean matrices is proposed, combining a Richardson-Leja spectral filter with a novel version of the Davidson method.

The method is exemplified on two problems from chemical physics, namely highly excited eigenstates of the Rubidium diatom (N=1024) and water (N=131072) molecules.

On the average less then 2.5 outer recursions per eigenstate are needed. For each outer Davidson recursion, less then 20 inner filter recursions per eigenstate are needed on the average.