Technical Aside:
The Power Method for Approximating Eigenvectors (and Eigenvalues)
Although the determination of exact eigenvalues and eigenvectors requires
considerable computation, the following iterative algorithm converges with
reasonable efficiency to the eigenvector that corresponds to the largest
eigenvalue:
Assumptions and Notation:

A is a (nonsingular) N × N matrix.

A has N linearly independent eigenvectors.

Unit eigenvectors B_{1}, B_{2}, ..., B_{N}
have eigenvalues λ_{1}, λ_{2}, ...,
λ_{N}.

The eigenvectors and eigenvalues have been ordered, so that
λ_{1} > λ_{2} ≥ ... ≥
λ_{N}
(Note we assume λ_{1} ≠ λ_{2} .)
created: 10 February 2007
last revised: 15 February 2007

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