  We investigate the equation of state w(z) in a non-parametric form using the
latest compilations of distance luminosity from SNe Ia at high z. We combine
the inverse problem approach with a Monte Carlo to scan the space of priors. On
the light of these high redshift supernova data sets, we reconstruct w(z). A
comparison between a sample including the latest results at z>1 and a sample
without those results show the improvement achieved by observations of very
high z supernovae. We present the prospects to measure the variation of dark
energy density along z by this method.
