Rayleigh-schrödinger perturbation theory: Practical implementation of matrix and vector formalisms and description of an heuristic sufficiency convergence criterion

Starting from previous work, where Rayleigh-Schrödinger perturbation theory has been reformulated in matrix form, a practical algorithm implementation is described using both full matrix and vector alternatives. An heuristic convergence sufficiency criterion based on Gershgorin discs is also presented. Some numerical examples related to atomic CI computations are reported to illustrate the theoretical framework.