Further variation diminishing properties of Bernstein polynomials on triangles
The author gives a new definition of the `variation' of a surface which generalizes those considered previously. See \textit{G. Chang} and \textit{J. Hoschek}, Multivariate Approximation Theory III, Proc. Conf. Oberwolfach/Ger. 1985, ISNM 75, 61-70 (1985; Zbl 0563.41008). It is shown that the variation of a Bernstein polynomial on a triangle is bounded by that of its Dézier net, and conditions are derived under which the bound is attained. A bound is given for the variation of the Bézier net in terms of the variation of the function itself. These results lead to variation diminishing properties of certain approximation operators involving polyhedral splines.
scientific article; zbMATH DE number 4032290