Shape preserving approximations by polynomials and splines
A review of shape preserving methods and algorithms for approximating univariate functions or discrete data is presented. Monotonicity and/or convexity preserving interpolations by polynomials, polynomial and rational polynomial splines are presented. Inter alia the Fritsch-Carlson method is discussed in details [cf. \textit{F. N. Fritsch} and \textit{R. E. Carlson}, SIAM, J. Numer. Anal. 17, 238-246 (1980; Zbl 0423.65011)]. Splines of lower degree are mainly considered [cf. \textit{R. Delbourgo} and \textit{J. A. Gregory}, SIAM, J. Sci. Stat. Comput. 6, 967-976 (1985; Zbl 0586.65006)]. Some other shape preserving approximating methods like approximation by positive linear operators are also discussed by the authors [cf. \textit{R. A. DeVore}, The approximation of continuous functions by positive linear operators, Lect. Notes Math. 293 (1972; Zbl 0276.41011)].
monotonicity and/or convexity preserving interpolations
scientific article; zbMATH DE number 1067160
scientific article