We present a new algorithm for building activation maps and localizing activation sites. In our approach the activation front is modeled as an anisotropic eikonal equation on a surface and the activation sites as the sources of this eikonal equation. The observations used to solve this inverse problem are obtained by electrical measurements on the torso surface, as could be performed by electrodes on a vest. We minimize a quadratic cost function measuring the mismatch between the observations and the predictions of the model. To this purpose we compute the sensitivity of the arrival times of the eikonal equation with respect to the source locations and with respect to the conductivity map. These sensitivities are evaluated by using fast algorithms: the Heat method and the Vector Heat Method. These fast numerical methods present the advantage to avoid to compute geodesics on the heart surface one by one, which would require a much higher computational cost. We present numerical tests in realistic 3D torso and heart geometries with in-silico data to assess the validity of our appproach.