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Mathematics-Online problems:

Interactive Problem 237: Bernstein-Basis

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#./interaufg237_en.tex#Show, that the Bernstein-polynomials

$\displaystyle b_0(t)=(1-t)^2, \qquad b_1(t)=2t(1-t) \qquad {\mbox{and}} \qquad b_2(t)=t^2 $

form a basis for the space of all polynomials of degree $ \leq 2$. Find a representation of the monomials $ 1$, $ t$ and $ t^2$ according to that basis.

Solution: (Declare the coefficients as decimals)

$ 1$ $ =$ $ b_0(t)$ $ +$ $ b_1(t)$ $ +$ $ b_2(t)$    
$ t$ $ =$ $ b_0(t)$ $ +$ $ b_1(t)$ $ +$ $ b_2(t)$    
$ t^2$ $ =$ $ b_0(t)$ $ +$ $ b_1(t)$ $ +$ $ b_2(t)$    

   

(Authors: Höllig/Höfert)

see also:

  automatically generated: 3/12/2018