Admissible slopes for monotone and convex interpolation
In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of various \(C^ 1\) interpolants which ensure a desirable shape. We dicuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials, \(C^ 1\) monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.
scientific article; zbMATH DE number 4013207