TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Titi, Jihad
A1  - Garloff, Jürgen
T1  - Matrix methods for the tensorial Bernstein form
JF  - Applied Mathematics and Computation
N2  - 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.
KW  - Bernstein coefficient
KW  - Tensorial Bernstein form
KW  - Range enclosure
KW  - Subdivision
KW  - Interval polynomial
Y1  - 2019
SN  - 0096-3003
SS  - 0096-3003
U6  - https://doi.org/10.1016/j.amc.2018.08.049
DO  - https://doi.org/10.1016/j.amc.2018.08.049
VL  - 346
SP  - 254
EP  - 271
ER  -