In this paper, a fast iterative physical optics (FIPO) algorithm is proposed for analysis of scattering from electrically large objects involving multiple reflections. When the scenario to be analyzed is electrically very large, a Fast Far Field Approximation (FaFFA) algorithm, based on a domain decomposition of the scatterer surface, can be conveniently used to greatly speed-up the calculation of the induced currents at each step of the iterative procedure. In this work, an efficient and accurate interpolation scheme has been combined to the standard FaFFA algorithm implementation further reducing the complexity of the computation.