Bernstein polynomial

In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician Sergei Natanovich Bernstein.

For the Bernstein polynomial in D-module theory, see Bernstein–Sato polynomial.

Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves.

A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm.

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