ISSN:
1432-2234
Keywords:
Generalized perturbed eigenvalue equation
;
Low rank perturbation
;
Piecewise local perturbations
;
Non-Hermitian matrices
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Summary The problem of finding eigenvalues and eigenstates of the generalized perturbed eigenvalue equation $$\left( {\mathbb{B} + \mathbb{V}} \right)$$ Ψ = g3(ℂ+ℙ)Ψ is considered. The eigenvalues and the eigenstates of the unperturbed eigenvalue equation $$\mathbb{B}$$ φ = λℂφ are assumed to be known. Matrices $$\mathbb{B},\mathbb{V}$$ , ℂ and ℙ can be arbitrary, except for the requirement that ℂ be nonsingular and that the eigenstates of the unperturbed equation be complete. It is shown that the eigenvalues and the eigenstates of the perturbed equation can be easily obtained if the rank of the generalized perturbation $$\left\{ {\mathbb{V},\mathbb{P}} \right\}$$ , ℙ is small. A special case of low rank perturbations are piecewise local perturbations which are common in physics and chemistry. If the perturbation is piecewise local with fixed localizability, the operation count for the derivation of a single eigenvalue and/or a single eigenstate is $$\mathcal{O}$$ (n). If the perturbation has a fixed rank, the operation count for the derivation of all eigenvalues and/or all eigenstates is $$\mathcal{O}$$ (n 2).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00529933
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