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Necessary and sufficient conditions are derived for a cubic to be monotone on an interval. These conditions are used to develop an algorithm which constructs a visually pleasing monotone piecewise cubic interpolant to monotone data. Several examples are given which compare this algorithm with other interpolation methods.
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Fritsch et al. (Tue,) studied this question.
www.synapsesocial.com/papers/69dab51f34ded318bb6847df — DOI: https://doi.org/10.1137/0717021
F.N. Fritsch
R.E. Carlson
SIAM Journal on Numerical Analysis
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