TY - JOUR
A1 - Titi, Jihad
A1 - Hamadneh, Tareq
A1 - Garloff, Jürgen
T1 - Convergence of the Simplicial Rational Bernstein Form
JF - Modelling, Computation and Optimization in Information Systems and Management Sciences
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 359)
N2 - Bernstein polynomials on a simplex V are considered. The expansion of a given polynomial p into these polynomials provides bounds for range of p over V. Bounds for the range of a rational function over V can easily be obtained from the Bernstein expansions of the numerator and denominator polynomials of this function. In this paper it is shown that these bounds converge monotonically and linearly to the range of the rational function if the degree of the Bernstein expansion is elevated. If V is subdivided then the convergence is quadratic with respect to the maximum of the diameters of the subsimplices.
KW - Bernstein polynomial
KW - simplex
KW - range bounds
KW - rational function
KW - degree elevation
Y1 - 2015
UR - http://www-home.htwg-konstanz.de/%7Egarloff/Paper95_MCO2015_Titi_Hamadneh_Garloff(1).pdf
U6 - http://dx.doi.org/10.1007/978-3-319-18161-5
SP - 433
EP - 441
ER -