An energy-scale-dependent approximation, that allows to resolve low energy features embedded in a high energy background, is reviewed. The Kondo and Anderson models are studied and fully self-consistently resolved as significative examples. A Kondo-like peak is obtained at low enough temperatures. The method is shown to be capable to reproduce the exact results with very low numerical effort and it is applicable for any value of the external parameters.

PACS numbers: 75.50.Ee, 75.30.Et, 75.25.+z, 75.50.--y