On multivariate polynomials in Bernstein-Bézier form and tensor algebra (Q651114)
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scientific article; zbMATH DE number 5987778
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On multivariate polynomials in Bernstein-Bézier form and tensor algebra |
scientific article; zbMATH DE number 5987778 |
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On multivariate polynomials in Bernstein-Bézier form and tensor algebra (English)
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8 December 2011
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A multilinear tensor notation is presented here to describe blossoms of multivariate polynomials in Bernstein-Bézier form. Such a blossom can be written as a collection of tensor-vector products. It is observed that the computation of these products can be interpreted as applying the (multi-affine) de Casteljau algorithm. Tensor algebra can thus be used for manipulating polynomials. As one of the applications the author considers Hermite interpolation with polynomials and splines [cf. \textit{H. Speleers}, Comput. Aided Geom. Design 27, 438--457 (2010; Zbl 1210.65027)].
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multivariate polynomials
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Bernstein-Bézier forms
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blossoming
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multilinear algebra
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tensors
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de Casteljau algorithm
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Hermite interpolation
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splines
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