Relative perturbation theory for definite matrix pairs and hyperbolic eigenvalue problem

2015 ◽  
Vol 98 ◽  
pp. 106-121 ◽  
Author(s):  
Ninoslav Truhar ◽  
Suzana Miodragović
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Relative Perturbation Theory

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

2003 ◽  
Vol 2003 (9) ◽  
pp. 459-485
Author(s):  
Brian J. McCartin
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Symmetric Matrix ◽  
Comprehensive Treatment ◽  
Matrix Eigenvalue Problem ◽  
Degenerate Problem ◽  
Matrix Eigenvalue ◽  
Penrose Pseudoinverse ◽  
Schrödinger Perturbation

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.

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