We discuss a natural way to deene barycentric coordinates associated with circular arcs. This leads to a theory of Bernstein-B ezier polynomials which parallels the familiar interval case, and which has close connections to trigonometric polynomials. x1. Introduction Bernstein-B ezier (BB-) polynomials deened on an interval are useful tools for constructing piecewise functional and parametric c...

We describe an algorithm which can efficiently evaluate Bernstein-Rabin-Winograd (BRW) polynomials. The presently best known complexity of evaluating a BRW polynomial on m ≥ 3 field elements is bm/2c field multiplications. Typically, a field multiplication consists of a basic multiplication followed by a reduction. The new algorithm requires bm/2c basic multiplications and 1 + bm/4c reductions....

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

Algebraic expressions of the Bernstein-Rabin-Winograd-polynomials, when defined over the field of the rational numbers, are obtained by recursion.

First we give a compact treatment of the Jacobi polynomials on a simplex in IR which exploits and emphasizes the symmetries that exist. This includes the various ways that they can be defined: via orthogonality conditions, as a hypergeometric series, as eigenfunctions of an elliptic pde, as eigenfunctions of a positive linear operator, and through conditions on the Bernstein–Bézier form. We the...

Bernstein and Markov-type inequalities are discussed for the derivatives of trigonometric and algebraic polynomials on general subsets of the real axis and of the unit circle. It has recently been proven by A. Lukashov that the sharp Bernstein factor for trigonometric polynomials is the equilibrium density of the image of the set on the unit circle under the mapping t → e. In this paper Lukasho...