[poster]

I would like to implement the Power Method for determining the dominant eigenvalue and eigenvector of a matrix in MATLAB.

Here's what I wrote so far:

%function to implement power method to compute dominant

%eigenvalue/eigenevctor

function [m,y_final]=power_method(A,x);

m=0;

n=length(x);

y_final=zeros(n,1);

y_final=x;

tol=1e-3;

while(1)

    mold=m;

 y_final=A*y_final;

 m=max(y_final);

 y_final=y_final/m;

 if (m-mold)
     break;

 end

end

end

With the above code, here is a numerical example:

 A=[1 1 -2;-1 2 1; 0 1 -1]



A =



     1     1    -2

    -1     2     1

     0     1    -1



>> x=[1 1 1];

>> x=x';

>> [m,y_final]=power_method(A,x);

>> A*x



ans =



     0

     2

     0

When comparing with the eigenvalues and eigenvectors of the above matrix in MATLAB, I did:

[V,D]=eig(A)



V =



    0.3015   -0.8018    0.7071

    0.9045   -0.5345    0.0000

    0.3015   -0.2673    0.7071





D =



    2.0000         0         0

         0    1.0000         0

         0         0   -1.0000

The eigenvalue coincides, but the eigenvector should be approaching [1/3 1 1/3]. Here, I get:

 y_final



y_final =



    0.5000

    1.0000

    0.5000

Is this acceptable to see this inaccuracy, or am I making some mistake?

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