Monotone and convex \(C^1\) Hermite interpolants generated by a subdivision scheme
The construction of \(C^1\) monotone and convex interpolants generated by the general subdivision scheme by \textit{J.-L. Merrien} in [Numer. Algorithms 2, 187-200 (1992; Zbl 0754.65011)] was studied. Whatever are the values and slopes of an increasing function \(f\) at the endpoints of a bounded interval \([a,b]\), it is always possible to construct a \(C^1\) increasing Hermite interpolant to \(f\). Similar results hold for a convex \(f\) and convex interpolant to \(f\) and furthermore for decreasing or concave functions \(f\).
scientific article; zbMATH DE number 1903847