Greedy algorithms in ridge approximation (gridge algorithms) are considered. Functions from the Gaussian weighted Hilbert space $L^2$ are approximated by linear combinations of ridge functions. The construction is iterative. On each step one more ridge function is added to the preceeding combination. This ridge function is selected greedily from the dictionary of ridge functions. The convergence rate of the gridge approximant is estimated in terms of the best approximations by algebraic polynomials. Theoretically, the gridge algorithms represent an iterative numerical method of Radon inversion.