When it is preferable to use Bernstein polynomials to approximate a continuous function instead of using the only following preliminary Numerical Analysis methods: "Lagrange Polynomials", "Simple finite differences operators".
One aspect of my question is to see that is there any predominance to use this method instead of those were mentioned even at very especial case? BERNSTEIN Polynomials are nice themselves and have lots of properties, but are they better to use for example in computer program or other situations too?


Thank Mr. Nikita Sidorov, Mr. Pietro Majer, Mr. Neeks, Mr. quid. but when I click to accept one, the other will non-accepted automatically, Why?


Your answers was nice all.



When we use Bernstein polynomials in application
The only practical advantage of Bernstein polynomials is their universality. They really work for any continuous function $f$. However, it is well known that if
$$
\|f-B\_n(f)\|\_\infty=o(1/n),\quad n\to\infty,
$$
then $f(x)=ax+b$. In other words, one cannot hope to approximate a non-linear function by a Bernstein polynomial with an error term better than $1/n$ - which is impractical. 


