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Matrix methods for the tensorial Bernstein form

  • In this paper, multivariate polynomials in the Bernstein basis over a box (tensorial Bernstein representation) are considered. A new matrix method for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, is presented and compared with existing methods. Also matrix methods for the calculation of the Bernstein coefficients over subboxes generated by subdivision of the original box are proposed. All the methods solely use matrix operations such as multiplication, transposition and reshaping; some of them rely on the bidiagonal factorization of the lower triangular Pascal matrix or the factorization of this matrix by a Toeplitz matrix. In the case that the coefficients of the polynomial are due to uncertainties and can be represented in the form of intervals it is shown that the developed methods can be extended to compute the set of the Bernstein coefficients of all members of the polynomial family.

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Metadaten
Author:Jihad TitiORCiD, Jürgen GarloffORCiDGND
DOI:https://doi.org/10.1016/j.amc.2018.08.049
ISSN:0096-3003
Parent Title (English):Applied Mathematics and Computation
Volume:346
Document Type:Article
Language:English
Year of Publication:2019
Release Date:2020/01/14
Tag:Bernstein coefficient; Interval polynomial; Range enclosure; Subdivision; Tensorial Bernstein form
First Page:254
Last Page:271
DDC functional group:500 Naturwissenschaften und Mathematik
Relevance:Peer reviewed Publikation in Master Journal List
Open Access?:Nein