  We study the single impurity Anderson model (SIAM) using the equations of
motion method (EOM), the non-crossing approximation (NCA), the one-crossing
approximation (OCA), and Wilson's numerical renormalization group (NRG). We
calculate the density of states and the linear conductance focusing on their
dependence on the chemical potential and on the temperature paying special
attention to the Kondo and Coulomb blockade regimes for a large range of model
parameters. We report that some standard approximations based on the EOM
technique display a rather unexpected poor behavior in the Coulomb blockade
regime even at high temperatures. Our study offers a critical comparison
between the different methods as well as a detailed compilation of the
shortcomings and limitations due the approximations involved in each technique,
thus allowing for a cost-benefit analysis of the different solvers that
considers both numerical precision and computational performance.
