In reply to Rick Wicklin.

Yes I meant that the magnitude are of the elements of the eigenvectors are like 2.335e-6, 3.876e-6.

And

The matrix is symmetric, all the eigenvalues are real, and the largest eigenvalue is not complex.
I am trying to calculate the maximum and minimum eigenvalues for a Hamiltonian matrix, which is like
[23 -1 0 0 -1]
[-1 45 -1 0 0]
[ 0 -1 32 -1 0]
[ 0 0 -1 76 -1]
[ -1 0 0 -1 51]

For a small matrix like this, the result converges within 200 iterations. and the values do not vary between two successive simulations.
So that should happen for all hamiltonian matrices, even if they are larger.
So i guess for 150k X 150k matrix, it requires more number of iterations.

I was not considering the relative change, I will have to incorporate it into my code then,
Thanks, for your help.