TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Titi, Jihad
A1  - Garloff, Jürgen
T1  - Matrix methods for the simplicial Bernstein representation and for the evaluation of multivariate polynomials
JF  - Applied Mathematics and Computation
N2  - In this paper, multivariate polynomials in the Bernstein basis over a simplex (simplicial Bernstein representation) are considered. Two matrix methods for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented. Also matrix methods for the calculation of the Bernstein coefficients over subsimplices generated by subdivision of the standard simplex are proposed and compared with the use of the de Casteljau algorithm. The evaluation of a multivariate polynomial in the power and in the Bernstein basis is considered as well. All the methods solely use matrix operations such as multiplication, transposition, and reshaping; some of them rely also on the bidiagonal factorization of the lower triangular Pascal matrix or the factorization of this matrix by a Toeplitz matrix. The latter one enables the use of the Fast Fourier Transform hereby reducing the amount of arithmetic operations.
KW  - Bernstein coefficient
KW  - Simplicial Bernstein representation
KW  - Range enclosure
KW  - Simplicial subdivision
KW  - Polynomial evaluation
Y1  - 2017
SN  - 0096-3003
SS  - 0096-3003
U6  - https://doi.org/10.1016/j.amc.2017.07.026
DO  - https://doi.org/10.1016/j.amc.2017.07.026
N1  - Volltextzugriff für Angehörige der Hochschule Konstanz möglich
IS  - 315
SP  - 246
EP  - 256
ER  -