A new approach to large-scale nuclear structure calculations, based on the
density matrix renormalization group (DMRG), is described. The method is te
sted in the context of a problem involving many identical nucleons constrai
ned to move in a single large-j shell and interacting via a pairing plus qu
adrupole interaction. In cases in which exact diagonalization of the Hamilt
onian is possible, the method is able to reproduce the exact results for th
e ground-state energy and the energies of low-lying excited states with ext
reme precision. Results are also presented for a model problem in which exa
ct solution is not feasible.