Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online problems:

Interactive Problem 237: Bernstein-Basis


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

#./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