  I report results of a density matrix renormalization group (DMRG) study of a
model for the two dimensional spin-gapped system CaV$_4$O$_9$. This study
represents the first time that DMRG has been used to study a two dimensional
system on large lattices, in this case as large as $24\times 11$, allowing
extrapolation to the thermodynamic limit. I present a substantial improvement
to the DMRG algorithms which makes these calculations feasible.
