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An explicit representation of a C1 piecewise rational cubic function is developed which can be used to solve the problem of shape preserving interpolation. It is shown that the interpolation method can be applied to convex and/or monotonic sets of data and an error analysis of the interpolant is given. The scheme includes, as a special case, the monotonic rational quadratic interpolant considered by the authors in 1 and 5. However, the requirement of convexity necessitates the generalization to the rational cubic form employed here.
Delbourgo et al. (Tue,) studied this question.