  The numerical renormalization group (NRG) is rephrased as a variational
method with the cost function given by the sum of all the energies of the
effective low-energy Hamiltonian. This allows to systematically improve the
spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of
similarities to the density matrix renormalization group (DMRG) when targeting
many states, and this synergy of NRG and DMRG combines the best of both worlds
and extends their applicability. We illustrate this approach with simulations
of a quantum spin chain and a single impurity Anderson model (SIAM) where the
accuracy of the effective eigenstates is greatly enhanced as compared to the
NRG, especially in the transition to the continuum limit.
