Based on Parameter Equation Function Rational Spline Interpolation with the Shape Preserved

A rational cubic spline function (3/2) involving two shape parameters is presented, and is applied to the interpolation problem with the data that its type is parameter equation function. Based on it, we deduce a sufficient condition for sign preserving and monotonicity preserving. Thus by adjusting the shape parameters, it can interactively modify the shape of the interpolation curve and meet the relevant requirement for shape preserving. Furthermore, the error estimation of the spline interpolant is also given. And the relevant numerical experiments confirm the previous conclusion.