Analogies between Higher-Order Analytical and Numerical Perturbation—Iteration Methods

Abstract

An analogy is pointed out between Hirschfelder's perturbation—iteration method for the determination of eigenvalues and eigenfunctions of linear differential operators and Roothaan's numerical procedure applicable to finite matrices. An analytical procedure analogous to Ostrowski's third‐order matrix method is shown to lead to unmanageable differential equations.