Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem

Brian J. McCartin

Journal of Applied Mathematics, 2003, vol. 2003, 1-27

Abstract:

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:424519

DOI: 10.1155/S1110757X03303092

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