Preliminary Application of Reinsch Splines to Cosmology: Transition
  Redshift Determination with Simulated OHD
  Many schemes have been proposed to perform a model-independent constraint on
cosmological dynamics, such as nonparametric dark energy equation of state
(EoS) \omega(z) or the deceleration parameter q(z). These methods usually
contain derivative processes with respect to observational data with noise.
However, it still remains remarkably uncertain when one estimates the numerical
differentiation, especially the corresponding truncation errors. In this work,
we introduce a global numerical differentiation method, first formulated by
Reinsch(1967), which is smoothed by cubic spline functions. The optimal
solution is obtained by minimizing the functional \Phi(f). To investigate the
potential of the algorithm further, we apply it to the estimation of the
transition redshift z_{t} with simulated expansion rate E(z) based on
observational Hubble parameter data(OHD). An effective method to determine the
free parameter S appearing in Reinsch Splines is provided.
