Abstract
A definition is given of the “variation” of a surface which generalizes those considered previously. It is then shown that the variation of a Bernstein polynomial on a triangle is bounded by that of its Bézier net and conditions are derived under which the bound is attained. A bound is also given for the variation of the Bézier net in terms of the variation of the function itself. Finally, it is mentioned how these results lead to variation diminishing properties of certain approximation operators involving polyhedral splines.
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Communicated by Wolfgang Dahmen.
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Goodman, T.N.T. Further variation diminishing properties of Bernstein polynomials on triangles. Constr. Approx 3, 297–305 (1987). https://doi.org/10.1007/BF01890572
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DOI: https://doi.org/10.1007/BF01890572