  We reconstruct the viable f(G) gravity models from the observations and
provide the analytic solutions that well describe our numerical results. In
order to avoid unphysical challenges that occur during the numerical
reconstruction, we generalize f(G) models into f(GA), which is the simple
extension of f(G) models with the introduction of a constant A parameter. We
employ several observational data together with the stability condition, which
reads d2f/dG2 > 0 and must be satisfied in the late-time evolution of the
universe, to give proper initial conditions for solving the perturbation
equation. As a result, we obtain the analytic functions that match the
numerical solutions. Furthermore, it might be interesting if one can find the
physical origin of those analytic solutions and its cosmological implications.
