Difference between revisions of "Bernstein B"
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| − | The Bernstein polynomials $ | + | The Bernstein basis polynomials $b_k^n$ are defined by |
| − | $$ | + | $$b_k^n(x)={n \choose k} x^k (1-x)^{n-k},$$ |
| − | where ${n \choose k}$ denotes a [[Binomial coefficient]]. | + | where ${n \choose k}$ denotes a [[Binomial coefficient]]. A Bernstein polynomial $B_n^k$ is defined as a linear combination of Bernstein basis polynomials, i.e. |
| + | $$B_n^k(x) = \displaystyle\sum_{i=0}^n \beta_i b_{i,n},$$ | ||
| + | where $\beta_i \in \mathbb{R}$. | ||
=Properties= | =Properties= | ||
=External links= | =External links= | ||
| − | [https://people.sc.fsu.edu/~jburkardt/py_src/bernstein_polynomial/bernstein_polynomial.html] <br /> | + | [https://people.sc.fsu.edu/~jburkardt/py_src/bernstein_polynomial/bernstein_polynomial.html BERNSTEIN_POLYNOMIAL ] <br /> |
=References= | =References= | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 01:54, 26 November 2017
The Bernstein basis polynomials $b_k^n$ are defined by $$b_k^n(x)={n \choose k} x^k (1-x)^{n-k},$$ where ${n \choose k}$ denotes a Binomial coefficient. A Bernstein polynomial $B_n^k$ is defined as a linear combination of Bernstein basis polynomials, i.e. $$B_n^k(x) = \displaystyle\sum_{i=0}^n \beta_i b_{i,n},$$ where $\beta_i \in \mathbb{R}$.
