Best approximation of continuous function uniformly by polynomials

Best approximation of continuous function uniformly by polynomials [closed]

Is there any polynomials that could approximate any continuous function uniforly apart of Bernstien polynomials?

flag	asked Dec 14 2011 at 19:11 nada 1

	See en.wikipedia.org/wiki/Polynomial_interpolation – Ryan Budney Dec 14 2011 at 19:25
	You could also use Fourier series and approximate the resulting exponentials by truncating their Taylor series (although note that the partial sums $S_N$ of the Fourier series do not always work, you need the Cesaro averages $\sigma_N$). However this is not very efficient if you want the lowest degree polynomials (but then, nor are the Bernstein polynomials; they are more of theoretical interest). There are many other ways to find approximating polynomials; however, you need to specify minimum degree or some other additional properties you are interested in. – Zen Harper Dec 15 2011 at 3:45
	You could also look at en.wikipedia.org/wiki/Approximation_theory – Zen Harper Dec 15 2011 at 3:46
	I think people often take "best" to mean "smallest degree" for a specified maximum error $\epsilon$, but maybe there are other criteria of more interest to you; you should say so. – Zen Harper Dec 15 2011 at 3:48