Multivariate Bernstein polynomials and convexity

DOI10.1016/0167-8396(91)90031-6zbMath0756.41029OpenAlexW2021309923MaRDI QIDQ1183539

Thomas Sauer

Publication date: 28 June 1992

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-8396(91)90031-6

zbMATH Keywords

Bernstein polynomialsaxial convexitypolyhedral convexityunivariate convex function

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximation by positive operators (41A36)

Related Items

The genuine Bernstein-Durrmmeyer operator on a simplex, Shape criteria of Bernstein-Bézier polynomials over simplexes, On the composition and decomposition of positive linear operators (V), A comparison of dependence function estimators in multivariate extremes, Axially parallel subsimplices and convexity, Bézier nets, convexity and subdivision on higher-dimensional simplices, Improving certain Bernstein-type approximation processes, Shape restriction of the multi-dimensional Bernstein prior for density functions, Multivariate Bernstein operators and redundant systems, Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials, Convexity preserving splines over triangulations, Optimized refinable enclosures of multivariate polynomial pieces, On a class of polynomial triangular macro-elements, Monotonicity preservation on triangles, Approximation properties of bivariate α-fractal functions and dimension results

Cites Work

• The convexity of Bernstein polynomials over triangles
• An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
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