  In this paper, we extend the recently developed reduced collocation method
\cite{ChenGottlieb} to the nonlinear case, and propose two analytical
preconditioning strategies. One is parameter independent and easy to implement,
the other one has the traditional affinity with respect to the parameters which
allows for efficient implementation through an offline-online decomposition.
Overall, the preconditioning improves the quality of the error estimation
uniformly on the parameter domain, and speeds up the convergence of the reduced
solution to the truth approximation.
