Journal of Applied Mathematics

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

Brian J. McCartin

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2003, Number 9 (2003), 459-485.

Dates
First available in Project Euclid: 15 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.jam/1063629206

Digital Object Identifier
doi:10.1155/S1110757X03303092

Mathematical Reviews number (MathSciNet)
MR2005052

Zentralblatt MATH identifier
1081.65514

Subjects
Primary: 15A18: Eigenvalues, singular values, and eigenvectors 65F15

Citation

McCartin, Brian J. Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem. J. Appl. Math. 2003 (2003), no. 9, 459--485. doi:10.1155/S1110757X03303092. https://projecteuclid.org/euclid.jam/1063629206


Export citation