Finding the Smallest Eigenvalue with Power Iteration in MatLab

[liquidFuzz]

I'm tinkering with a code snippet where a part finds eigenvalues.

eig(A);

The thing is, I tried to do it not using eig() to grasp this and got stuck. Could anyone shed some light on this..? How do I find the smallest eigenvalue?

 

[liquidFuzz]

Hmm... I might be a little bit closer. This seems to compute the biggest eigenvalue.

    while (abs(lambda - lambda_old) > tol)
        lambda_old = lambda;
        lambda = y'*A*z/norm(z, 2);   %this part should be altered to compute the smallest.
    end

 

[Pythagorean]

d = eig(A) returns a vector of the eigenvalues of matrix A (notice, I'm assigning it to 'd')

to find the smallest value in a vector:

smallest = min(d)

so, all you really have is:

d = eig(A)
sm = min(d)

where sm is the smallest eigenvalue.
Not quite what MATLAB calls the smallest when mixing complex numbers with real numbers.

 

[Pythagorean]

ok, weird... so:

according to min, the first entry in A is the "smallest"

A =

  1.000000000000000 + 1.000000000000000i
 -1.000000000000000 + 1.000000000000000i

>> min(A)

ans =

  1.000000000000000 + 1.000000000000000i

but according to the lessthan sign, the second entry is the "smallest"

 >> if A(1) < A(2)
dips('YES')
end
>>if A(2) < A(1)
disp('YES')
end
YES

 

[liquidFuzz]

I'm trying to set up a power iteration - not using eig(). I'm pretty sure I get the power iteration right, but the inverted power iteration to get the smallest..?