  We perform a comprehensive study of the dark energy equation of state (EoS)
utilizing the model-independent Gaussian processes (GP). Using a combination of
the Union 2.1 data set, the 30 newly added H(z) cosmic chronometer data points
and Planck's shift parameter, we modify the usual GaPP code and provide a
tighter constraint on the dark energy EoS than the previous literature about GP
reconstructions. Subsequently, we take the "controlling variable method" to
investigate directly the effects of variable matter density parameter
$\Omega_{m0}$, variable cosmic curvature $\Omega_{k0}$ and variable Hubble
constant $H_0$ on the dark energy EoS, respectively. We find that too small or
large $\Omega_{m0}$, $\Omega_{k0}$ and $H_0$ are all disfavored by our GP
reconstructions based on current cosmological observations. Subsequently, we
find that variable $\Omega_{m0}$ and $\Omega_{k0}$ affect the reconstructions
of the dark energy EoS, but affect hardly the reconstructions of the normalized
comoving distance $D(z)$ and its derivatives $D'(z)$ and $D"(z)$. However,
variable $H_0$ affects the reconstructions of the dark energy EoS by affecting
obviously those of $D(z), D'(z)$ and $D"(z)$. Furthermore, we find that the
results of our reconstructions support substantially the recent local
measurement of $H_0$ reported by Riess et al.
