A simple method for the estimation of the lowest eigenvalues of symmetric matrices

Abstract

A simple method for the estimation of the lowest (highest) eigenvalues of very large symmetric matrices is shown, which is based on the combination of Peturbation Theory, the Kirzhnits method, and the so called Principle of Minimal Sensitivity. The procedure could be employed in order to regularize perturbation series arising in Physics such as, for example, the Moller-Plesset series for the correlation energy of atoms or molecules.