On multivariate polynomials in Bernstein-Bézier form and tensor algebra
type: Item
instance of: scholarly article
title: On multivariate polynomials in Bernstein-Bézier form and tensor algebra
zbMATH Open document ID: 1233.65016
author: Hendrik Speleers
published in: Journal of Computational and Applied Mathematics
publication date: 2011-12-08T00:00:00Z
review text: 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)].
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 5987778
zbMATH Keywords: multivariate polynomials
zbMATH Keywords: Bernstein-Bézier forms
zbMATH Keywords: blossoming
zbMATH Keywords: multilinear algebra
zbMATH Keywords: tensors
zbMATH Keywords: de Casteljau algorithm
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: splines
MaRDI profile type: Publication
full work available at URL: j.cam.2011.04.032
OpenAlex ID: W1966118370
cites work: Q3776153
cites work: On the optimal stability of the Bernstein basis
cites work: Optimally stable multivariate bases
cites work: Evaluation algorithms for multivariate polynomials in Bernstein-Bézier form
cites work: Efficient evaluation of multivariate polynomials
cites work: Tensor Decompositions and Applications
cites work: Symmetric Tensors and Symmetric Tensor Rank
cites work: Decomposition of quantics in sums of powers of linear forms
cites work: A characterization theorem of multivariate splines in blossoming form
cites work: Blossoms are polar forms
cites work: A Multilinear Singular Value Decomposition
cites work: Piecewise Quadratic Approximations on Triangles
cites work: Smooth macro-elements based on Powell--Sabin triangle splits
cites work: \(C^ r\)-finite elements of Powell-Sabin type on the three direction mesh
cites work: Macro-elements and stable local bases for splines on Powell-Sabin triangulations
cites work: Spline Functions on Triangulations
cites work: Composite finite elements of class \(C^ k\)
cites work: On calculating normalized Powell-Sabin B-splines
cites work: A normalized basis for quintic Powell-Sabin splines
cites work: Quadratic spline quasi-interpolants on Powell-Sabin partitions
cites work: Interpolation with quintic Powell-Sabin splines
cites work: How to multiply matrices faster
DOI: 10.1016/J.CAM.2011.04.032
description: scientific article; zbMATH DE number 5987778