method (BRG) has the advantage of being conceptually and technically simple, but it lacks of numerical accuracy or may even produce wrong results. For this reason the analytical BRG methods were largely abandoned in the 80’s in favor of numerical methods such as the Quantum Monte Carlo approaches. In the last few years there has been new developments in the numerical RG methods motivated by a better understanding of the errors introduced by the splitting of the lattice into disconnected blocks. A first step was put forward in [@white-noack] where a combination of different periodic boundary conditions applied to every block lead to the correct energy levels of a simple tight-binding model. This method however has not been generalized to models describing interactions. Recently, we have clarified the role played by the boundary conditions in the real-space renormalization group method [@bc-germanyo] by constructing a new analytical BRG-method which is able to give the exact ground state of the model and the correct $1/N^2$-law for the energy of the first excited state in the large $N$(size)-limit. A further step in the generalization to interacting models was undertaken by White in [@white] where a Density Matrix algorithm (DMRG) is developed. The main 