Brian J. M Cartin
Department of Applied Mathematics
Kettering University
1700 West Third Avenue, Flint, MI 48504-4898, USA
e-mail: [email protected]

Abstract.In this paper, a comprehensive treatment of analytic Rayleigh-Schrödinger perturbation theory for the symmetric eigenvalue problem [#!1!#], [#!2!#] is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus constituting the natural generalization of the procedure for linear perturbation of the symmetric eigenvalue problem [#!3!#]. 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. Along the way, we generalize the Dalgarno-Stewart identities [#!15!#] from linear to analytic matrix perturbations. The general procedure is illustrated by an extensive example.

Received: September 12, 2005

AMS Subject Classification: 15A18, 65F15

Key Words and Phrases: spectral perturbation theory, symmetric eigenvalue problem, Moore-Penrose pseudoinverse

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 24
Issue: 2