  A model--independent approach to dark energy is here developed by considering
the determination of its equation of state as an inverse problem. The
reconstruction of w(z) as a non--parametric function using the current SNe Ia
data is explored. It is investigated as well how results would improve when
considering other samples of cosmic distance indicators at higher redshift.
This approach reveals the lack of information in the present samples to
conclude on the behavior of w(z) at z > 0.6. At low level of significance a
preference is found for w_{0} < -1 and w'(z) > 0 at z ~ 0.2--0.3. The solution
of w(z) along redshift never departs more than 1.95\sigma from the cosmological
constant w(z)=-1, and this only occurs when using various cosmic distance
indicators. The determination of w(z) as a function is readdressed considering
samples of large number of SNe Ia as those to be provided by SNAP. It is found
an improvement in the resolution of w(z) when using those synthetic samples,
which is favored by adding data at very high z. Though the set of degenerate
solutions compatible with the data can be retrieved through this method, these
degeneracies in the solution will difficult the physical interpretation of the
results. Through this approach, we have explored as well the gain in
information in w(z) and the quality of the inversion achieved using different
data sets of cosmic distance indicators.

High Energy Physics - Phenomenology;Astrophysics