  We present variational estimates for the low-lying energies of a simple
matrix model that approximates $SU(3)$ Yang-Mills theory on a three-sphere of
radius $R$. By fixing the ground state energy, we obtain the (integrated)
renormalization group (RG) equation for the Yang-Mills coupling $g$ as a
function of $R$. This RG equation allows to estimate the masses of other
glueball states, which we find to be in excellent agreement with lattice
simulations.
