Abstract
Bernstein polynomials on a simplex V are considered. The expansion of a given polynomial p into these polynomials provides bounds for the range of p over V. Bounds for the range of a rational function over V can easily 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.
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Titi, J., Hamadneh, T., Garloff, J. (2015). Convergence of the Simplicial Rational Bernstein Form. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-18161-5_37
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DOI: https://doi.org/10.1007/978-3-319-18161-5_37
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