Geodesic
Monotone and convex interpolation by weighted cubic splines
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1610-1621

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Algorithms for interpolating by weighted cubic splines are constructed with the aim of preserving the monotonicity and convexity of the original discrete data. The analysis performed in this paper makes it possible to develop two algorithms with the automatic choice of the shape-controlling parameters (weights). One of them preserves the monotonicity of the data, while the other preserves the convexity. Certain numerical results are presented. 
@article{ZVMMF_2013_53_10_a1,
     author = {B. I. Kvasov},
     title = {Monotone and convex interpolation by weighted cubic splines},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1610--1621},
     publisher = {mathdoc},
     volume = {53},
     number = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a1/}
}
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B. I. Kvasov. Monotone and convex interpolation by weighted cubic splines. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1610-1621. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a1/