Just finished a nice little matlab script that gives me the dominant eigenvalue (with an error of at most 10^-7) and eigenvector of a 3x3 matrix, using the power method.
However, it's giving me the correct eigenvalue, but the negative of the eigenvector (-b instead of b).
Here's my script
a=[9 5 1;8 -5 9;-9 -2 -2];
b=[1;1;1];function bnew=powermethod(a,b)
bnew=[0;0;0]; c=0; itterations = 0;
while c==0
itterations = itterations + 1;
bnew=a*b/norm(a*b);
d=a*b; e=a*bnew;error = abs( (d(1)/b(1)) - (e(1)/bnew(1)) );
if error<10^-7
c=1;
end
b=bnew;
end
fprintf('\n Script took %d itterations to converge.\n', itterations);
fprintf('\n Eigenvalue is %d.\n', e(1)/bnew(1));
end
I know this is pushing it a bit, but thought someone might be able to see what's going on. Cheers.
