Shape-preserving 𝐶² cubic polynomial interpolating splines

Fiorot, J.-C.; Tabka, J.

doi:10.1090/S0025-5718-1991-1079015-1

Shape-preserving $C^ 2$ cubic polynomial interpolating splines
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by J.-C. Fiorot and J. Tabka PDF

Math. Comp. 57 (1991), 291-298 Request permission

Abstract:

In this paper we propose a method to construct shape-preserving ${C^2}$ cubic polynomial splines interpolating convex and/or monotonic data. For such given data, the existence or nonexistence of such interpolating splines can be expressed in terms of existence or nonexistence of solutions for a system of linear inequalities in two unknowns.

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