The main contribution of this paper is to present a new set of approximate analytical solutions for the parameters of a photovoltaic (PV) five-parameter double-diode model that can be used as initial values for the numerical solutions based on the Newton-Raphson method. The proposed formulations are developed based on only the limited information given by the PV manufacturers, i.e., the open-circuit voltage (V-oc), the short circuit current (I-sc), and the current and voltage at the maximum power point (I-m and V-m). Compared with the existing techniques that require the entire experimental I-V curve or additional information such as the slope of the I-V curves of the open circuit and the short circuit points, the proposed technique is quite independent of these additional data, and, it is therefore, a low cost and fast parameter extraction method. The accuracy of the theoretical I-V curves is evaluated through the comparison of the simulation results and experimental data. The results of the application of the proposed technique to different PV modules show the accuracy and validity of the proposed analytical-numerical method.