A fast direct method of mass reconstruction for gravitational lenses

Statistical analyses of observed galaxy distortions are often used to reconstruct the mass distribution of an intervening cluster responsible for gravitational lensing. In current projects, distortions of thousands of source galaxies have to be handled efficiently; much larger data bases and more massive investigations are envisaged for new major observational initiatives. In this article we present an efficient mass reconstruction procedure, a direct method that solves a variational principle noted in an earlier paper, which, for rectangular fields, turns out to reduce the relevant execution time by a factor from 100 to 1000 with respect to the fastest methods currently used, so that for grid numbers N = 400 the required CPU time on a good workstation can be kept within the order of 1 second. The acquired speed also opens the way to some long-term projects based on simulated observations (addressing statistical or cosmological questions) that would be, at present, practically not viable for intrinsically slow reconstruction methods.