The previous discussion explains the following Power Method for computing a unit eigenvector corresponding to the dominent eigenvalue of a matrix A:

     Start with an arbitrary vector V
         (we hope V has a component related to the largest eigenvector)
     Scale V to get a unit vector S
     Repeat
        Compute R = A S
        Scale R to get a unit vector R'
        compute r = |R' - S|
        set S = R'
     Until (r < ε)

     Return S as eigenvector approximation
        (Note that |R| / |S| is an approximation to λ1)

As noted, this coverges to the dominant eigenvector under modest assumptions.

created: 10 February 2007 last revised: 15 February 2007

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