 Heavy-ball rate for a two-eigenvalue diagonal quadratic

For $A=\mathrm{diag}(1,\gamma )$, $\alpha =1/\gamma$, and $\beta =(1-{\gamma }^{-1/2}{)}^2$, every error-propagation block has spectral radius at most $1-{\gamma }^{-1/2}$, and equality occurs.