Constraints of the equation of state of dark energy from current and future observational data by piecewise parametrizations

The model-independent piecewise parametrizations (0-spline, linear-spline and cubic-spline) are used to estimate constraints of equation of state of dark energy ($w_{de}$) from current observational data (including SNIa, BAO and Hubble parameter) and the simulated future data. A combination of fitting results of $w_{de}$ from these three spline methods reveal essential properties of real equation of state $w_{de}$. It is shown that $w_{de}$ beyond redshift $z\sim0.5$ is poorly constrained from current data, and the mock future $\sim2300$ supernovae data give poor constraints of $w_{de}$ beyond $z\sim1$. The fitting results also indicate that there might exist a rapid transition of $w_{de}$ around $z\sim0.5$. The difference between three spline methods in reconstructing and constraining $w_{de}$ has also been discussed.