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 ^ { \prime } ( z ) > 0 at z \sim 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 .
The set of degenerate solutions compatible with the data can be retrieved through this method .