Adaptive optics (AO) systems under study for the future generation of telescopes have to cope with a huge number of degrees of freedom. This number N is typically 2 orders of magnitude larger than for the currently existing AO systems. An iterative method using a fractal preconditioning, has recently been suggested for a minimum-variance reconstruction in O (N ) operations. We analyze the efficiency of this algorithm for both the open-loop and the closed-loop configurations. We present the formalism and illustrate the assets of this method with simulations. While the number of iterations for convergence is around 10 in open-loop, the closed-loop configuration induces a reduction of the required number of iterations by a factor of 3 typically. This analysis also enhances the importance of introducing priors to ensure an optimal command. Closed-loop simulations demonstrate the loss of performance when no temporal priors are used. Besides, we discuss the importance of an accurate model for both the system and its uncertainties, so as to ensure a stable behavior in closed-loop.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.