Power Method in MATLAB
 

<p>I would like to implement the <a href="http://mathfaculty.fullerton.edu/mathews//n2003/PowerMethodMod.html" rel="nofollow">Power Method</a> for determining the dominant eigenvalue and eigenvector of a matrix in MATLAB.</p>

<p>Here's what I wrote so far:</p>

<pre><code>%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)<tol
break;
end
end
end
</code></pre>

<p>With the above code, here is a numerical example:</p>

<pre><code> 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
</code></pre>

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

<pre><code>[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
</code></pre>

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

<pre><code> y_final

y_final =

0.5000
1.0000
0.5000
</code></pre>

<p>Is this acceptable to see this inaccuracy, or am I making some mistake? </p>



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