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.