  We consider the partition function and correlation functions in the bosonic
and supersymmetric Yang-Mills matrix models with compact semi-simple gauge
group. In the supersymmetric case, we show that the partition function
converges when $D=4,6$ and 10, and that correlation functions of degree $k<
k_c=2(D-3)$ are convergent independently of the group. In the bosonic case we
show that the partition function is convergent when $D \geq D_c$, and that
correlation functions of degree $k < k_c$ are convergent, and calculate $D_c$
and $k_c$ for each group, thus extending our previous results for SU(N). As a
special case these results establish that the partition function and a set of
correlation functions in the IKKT IIB string matrix model are convergent.
