Residue-squaring iterative diagonalization methods for perturbation problems

A new method for the evaluation of the change in eigenvalues due to a perturbation of strength lambda is presented. It is a fast converging iterative method which, at the nth step, gives results accurate to order (2sup(n+1)-1) in lambda. Unlike the Rayleigh-Schroedinger perturbation theory in quantum mechanics, which becomes prohibitively cumbersome when carried to higher orders, the present method involves a routine which remains straightforward at all stages. (author)