Geodesic
Sufficient conditions for the comonotone interpolation of cubic $C^2$
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 3-13

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We consider the problem of interpolation of a function under the condition of the preservation of the nature of its piecewise monotonicity. We give sufficient conditions for the comonotone interpolation by a classical cubic $C^2$-spline in the representation based on the expansion of its first derivative in a basis consisting of $B$-splines. These conditions allow to determine whether the soobtained spline is comonotone without solving the interpolation problem. 
@article{MT_2011_14_2_a0,
     author = {V. V. Bogdanov},
     title = {Sufficient conditions for the comonotone interpolation of cubic $C^2$},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--13},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2011_14_2_a0/}
}
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V. V. Bogdanov. Sufficient conditions for the comonotone interpolation of cubic $C^2$. Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/MT_2011_14_2_a0/