Geodesic
Shape-Preserving Interpolation by Cubic Splines
Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 836-844

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We consider the problem of shape-preserving interpolation by cubic splines. We propose a unified approach to the derivation of sufficient conditions for the $k$‑monotonicity of splines (the preservation of the sign of any derivative) in interpolation of $k$-monotone data for $k=0,\dots,4$.
Keywords: cubic spline, shape-preserving interpolation, $k$‑monotonicity, $B$-spline, matrix with diagonal dominance. 
@article{MZM_2010_88_6_a3,
     author = {Yu. S. Volkov and V. V. Bogdanov and V. L. Miroshnichenko and V. T. Shevaldin},
     title = {Shape-Preserving {Interpolation} by {Cubic} {Splines}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {836--844},
     publisher = {mathdoc},
     volume = {88},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a3/}
}
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Yu. S. Volkov; V. V. Bogdanov; V. L. Miroshnichenko; V. T. Shevaldin. Shape-Preserving Interpolation by Cubic Splines. Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 836-844. http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a3/