关键词: 有理多项式, 插值, 凸函数, 单调函数, 保形

Abstract: A rational scheme for shape preserving interpolation to general data sets is given, which possesses the characteristics of the rational interpolation function such as simple form and parameters to be easily choosen. The parameters of the C2 interpolation to a convex data set can be easily found, with no need to resolve a nonlinear system. Error estimation is given, by using the best error estimation of Hermite interpolation. As the corollary, the error estimation for the convexity (and / or monotonicity ) preserving interpolation to convex (and / or monotonic) data is obtained. Furthermore, the parameters for C1 and C2 interpolation can be freely choosen within certain extent to adjust the shape of the interpolating curve or to obtain a better approximation to the original function that the data comes from.The rational shape preserving interpolation method in this paper has been used in the microcomputer CAD parallel system (based on Transputer) which is being developed.

Key words: rational polynomial, interpolation, convex function, monotonic function, shape-preserving