Properties
The Bernstein basis polynomials have the following properties:
- , if or .
- and where is the Kronecker delta function.
- has a root with multiplicity at point (note: if, there is no root at 0).
- has a root with multiplicity at point (note: if, there is no root at 1).
- for .
- .
- The derivative can be written as a combination of two polynomials of lower degree:
- The integral is constant for a given
- If, then has a unique local maximum on the interval at . This maximum takes the value:
- The Bernstein basis polynomials of degree form a partition of unity:
- By taking the first derivative of where, it can be shown that
- The second derivative of where can be used to show
- A Bernstein polynomial can always be written as a linear combination of polynomials of higher degree:
Read more about this topic: Bernstein Polynomial
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