The 40-meter size of the primary mirror of the European Extremely Large Telescope (E-ELT) aims at reaching new limits of light sensitivity, but also at significantly increasing the angular resolution of the observations. This high angular resolution will be available only if adaptive optics (AO) are built on the E-ELT to compensate for the noxious effects of atmosphere. Despite successful existing AO systems on the 10-m class telescopes, building AO systems on the E-ELT raises new challenges, in particular to solve in real-time the wavefront reconstruction and control. The wavefront reconstruction and control on the E-ELT is an inverse problem with large number of degrees of freedom (~ 10,000).  I present a fast algorithm to optimally solve the atmosphere reconstruction at the E-ELT scale, based on a fractal iterative method. The iterative aspect of the inverse problem approach  is highlighted to offer new prospects for AO system identification, and self-optimization of the AO correction during astrophysical observations.