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A method is presented for controlling the convexity of interpolant curves based on a rational cubic interpolating function with quadratic denominator. The key idea is that the uniqueness of the interpolating function for the given data is replaced by the uniqueness of the interpolating function for the given data and the parameters, so that for the given data the shape of the interpolating curve can be modified by selecting suitable parameters. Necessary and sufficient conditions are given for adjusting the convexity of the interpolating curve for given data. Examples are given and the optimal error estimation is given.
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Duan et al. (2003) studied this question.
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