Evaluation of the two-loop self-energy correction to the ground state energy of H-like ions to all orders in Zα

We present an evaluation of the complete gauge-invariant set of the two-loop self-energy diagrams carried out to all orders in the parameter $Z\alpha$. The calculation is performed for the ground state of H-like ions with $Z\ge 40$. As a result, we significantly improve the accuracy of theoretical values for the ground-state Lamb shift in high-Z H-like ions. We provide a compilation of various contributions to the ground-state energy of H-like ions and estimate uncertainties of the corresponding theoretical predictions