  An extension of the the density matrix renormalization group (DMRG) method is
presented. Besides the two groups or classes of block states considered in
White's formulation, the retained $m$ states and the neglected ones, we
introduce an intermediate group of block states having the following $p$
largest eigenvalues $\lambda_i$ of the reduced density matrix: $\lambda_1 \ge
>... \lambda_m \ge \lambda_{m+1}\ge ... \ge \lambda_{m+p}$. These states are
taken into account when they contribute to intrablock transitions but are
neglected when they participate in more delocalized interblock fluctuations.
Applications to one-dimensional models (Heisenberg, Hubbard and dimerized
tight-binding) show that in this way the involved computer resources can be
reduced without significant loss of accuracy. The efficiency and accuracy of
the method is analyzed by varying $m$ and $p$ and by comparison with standard
DMRG calculations. A Hamiltonian-independent scheme for choosing $m$ and $p$
and for extrapolating to the limit where $m$ and $p$ are infinite is provided.
Finally, an extension of the 3-classes approach is outlined, which incorporates
the fluctuations between the $p$ states of different blocks as a
self-consistent dressing of the block interactions among the retained $m$
states.
