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Which spaces for design? (English) Zbl 1157.65016

Author’s abstract: We determine the largest class of spaces of sufficient regularity which are suitable for design in the sense that they do possess blossoms. It is the class of all spaces containing constants of which the spaces derived under differentiation are quasi extended Chebyshev spaces, i.e., they permit Hermite interpolation, Taylor interpolation excepted. It is also the class of all spaces which possess Bernstein bases, or of all spaces for which any associated spline space does possess a B-spline basis. Note that blossoms guarantee that such bases are normalised totally positive bases. They even are the optimal ones.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D05 Numerical interpolation
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