Variation diminishing properties of Bernstein polynomials on triangles

DOI10.1016/0021-9045(87)90002-5zbMath0618.41007OpenAlexW2003570903MaRDI QIDQ1822287

Tim N. T. Goodman

Publication date: 1987

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(87)90002-5

zbMATH Keywords

Bernstein polynomialnet of Bézier

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Approximation by positive operators (41A36)

Related Items (11)

Further variation diminishing properties of Bernstein polynomials on triangles ⋮ Shape criteria of Bernstein-Bézier polynomials over simplexes ⋮ Bernstein-Bézier Galerkin-characteristics finite element method for convection-diffusion problems ⋮ A semi-Lagrangian Bernstein-Bézier finite element method for two-dimensional coupled Burgers' equations at high Reynolds numbers ⋮ A Bernstein-Bézier Lagrange-Galerkin method for three-dimensional advection-dominated problems ⋮ Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements ⋮ On boundedness inequalities in the variation of certain Schurer-type operators ⋮ Bézier nets, convexity and subdivision on higher-dimensional simplices ⋮ Is there a geometric variation diminishing property for B-spline or Bézier surfaces? ⋮ Monotonicity preservation on triangles ⋮ Convexity of Bézier nets on triangulations

Cites Work

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• Remarks on de la Vallée Poussin means and convex conformal maps of the circle
• The convexity of Bernstein polynomials over triangles

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