  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.
