  A nonperturbative method to obtain on- and off-site one-particle Green's
function is introduced and applied to noninteracting Hubbard model with next
nearest neighbor hopping and interacting Hubbard model in large dimensions, for
example. The former gives some lessons on the method and shows the advantage of
the method compared with continued fraction formalism. The latter is treated by
selecting important dynamic processes contributing to the Green's function when
correlation is strong. We consider the model in the Bethe lattice with large
connectivity. The dynamic processes describing on-site spin fluctuation clearly
shows metal-insulator transition in the paramagnetic ground state at half
filling.
