Pseudoinverse formulation of Rayleigh‐Schrödinger perturbationtheory for the symmetric matrix eigenvalue problem
Brian J. McCartin · Journal of Applied Mathematics · 2003
A comprehensive treatment of Rayleigh‐Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore‐Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix‐theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher‐order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example.