properties of Bernstein polynomial

The Bernstein polynomialsMathworldPlanetmath Bin(t) have the following properties:

0.1 Non negativity

The polynomialsPlanetmathPlanetmath are non-negative over the interval [0,1].

Bin(t)0  0t1

0.2 Symmetry

The set of polynomials of degree n is symmetricPlanetmathPlanetmathPlanetmathPlanetmath with respect to t=1/2.


0.3 Maximum

Each polynomial has only one maximum over the interval [0,1] at t=in.

0.4 Normalization

The set of polynomials of degree n forms a partition of unity.


0.5 Degree raising

A polynomial can always be written as a linear combinationMathworldPlanetmath of polynomials of higher degree.

Title properties of Bernstein polynomial
Canonical name PropertiesOfBernsteinPolynomial
Date of creation 2013-03-22 17:24:13
Last modified on 2013-03-22 17:24:13
Owner stitch (17269)
Last modified by stitch (17269)
Numerical id 10
Author stitch (17269)
Entry type Derivation
Classification msc 65D17