Richardson's iteration introduce a scalar $$\alpha$$ to the update formula:
$$\textbf{x}^{(k+1)} = \textbf{x}^{(k)} + \alpha \textbf{r}^{(k)}$$
And compute $$\alpha$$ by minimizing the spectral radius:
$$min_{\omega}\{\rho(B)\} = min_{\omega}\{\rho(I-\omega A)\}$$
As I,A do not change over the iterations, it might seem it exists only one (i.e. equal for all the iterations) $$\omega$$ making the max eigenvalue minimal, hence the spectral radius minimal. Since I know gradient method and conjugate gradient perform better by setting $$\alpha$$ dynamically, I am wondering what am I missing here. Is there any way to see through the spectral radius expression that gradient and conjugate gradient iterations converge faster?