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
Assumptions and Notation:
A is a (non-singular) N × N matrix.
A has N linearly independent eigenvectors.
Unit eigenvectors B1, B2, ..., BN
have eigenvalues λ1, λ2, ...,
The eigenvectors and eigenvalues have been ordered, so that
|λ1| > |λ2| ≥ ... ≥
(Note we assume |λ1| ≠ |λ2| .)
created: 10 February 2007|
last revised: 15 February 2007