Fritsch and Carlson [SIAM J. Numer. Anal., 17 (1980), pp. 238–246] developed an algorithm which produces a monotone C¹ piecewise cubic interpolant to a monotone function. We show that their algorithm yields a third-order approximation, while a modification is fourth-order accurate.
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Eisenstat et al. (1985) studied this question.
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