Direct Estimate for Bernstein Polynomials

Discrete Bernstein Inequalities for Polynomials

We study discrete versions of some classical inequalities of Berstein for algebraic and trigonometric polynomials. Mathematics subject classification (2010): 30C10, 41A17.

Division algorithms for Bernstein polynomials

Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for calculating the GCD of an arbitrary collection of univariate polynomials, and an algorithm for computing a μ-basis for the syzygy module of an arbitrary collection of univariate polynomials. Division algorithms for mult...

Bernstein Polynomials for Radiative Transfer Computations

In this paper we propose using planar and spherical Bernstein polynomials over triangular domain for radiative transfer computations. In the planar domain, we propose using piecewise Bernstein basis functions and symmetric Gaussian quadrature formulas over triangular elements for high quality radiosity solution. In the spherical domain, we propose using piecewise Bernstein basis functions over ...

Bernstein Inequalities for Polynomials with Constrained Roots

We prove Bernstein type inequalities for algebraic polynomials on the finite interval I := [−1, 1] and for trigonometric polynomials on R when the roots of the polynomials are outside of a certain domain of the complex plane. The case of real vs. complex coefficients are handled separately. In case of trigonometric polynomials with real coefficients and root restriction, the Lpsituation will al...

A companion matrix resultant for Bernstein polynomials