Dividing by \( (f_i^i +f_j^j -f_a^a -f_b^b) \) yields
$$ \begin{align} t_{ij}^{ab} &= t_{ij}^{ab} + \frac{\overline{H}_{ij}^{ab}}{f_i^i +f_j^j -f_a^a -f_b^b} \tag{36} \end{align} $$This equation is of the type \( t=f(t) \), and we solve it by iteration, i.e. we start with a guess \( t_0 \) and iterate \( t_{n+1}=f(t_n) \), and hope that this will converge to a solution. We take the perturbative result
$$ \begin{align} \tag{37} \left(t_{ij}^{ab}\right)_0 = \frac{\langle ab\vert V\vert ij\rangle}{f_i^i +f_j^j -f_a^a -f_b^b} \end{align} $$as a starting point, compute \( \overline{H}_{ij}^{ab} \), and find a new \( t_{ij}^{ab} \) from the right-hand side of Eq. (36). We repeat this process until the amplitudes (or the CCD energy) converge.