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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?

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