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Hello

If instead of equis point in Bernstein polynomials, we use Chebyshev points, What do you think?

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Could you please make more precise what you would like to ask. – quid Dec 17 2011 at 15:03
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 You can edit this question. Press the button below the auestion. Please do not do this via a new question. (If ever you should have major difficulties to edit, please at least do this sort of clarfication via an answer. But also this is only a last-resort solution.) – quid Dec 17 2011 at 15:39
I mean, If we insteaf of (k/N) points, k=o,....N we use Chebyshev points to approximate a continuous function uniformly by Bernstien polynomials. – nada Dec 17 2011 at 16:45
If we do that what? you have to ask a complete question for there to be any chance of it being answered! – Mariano Suárez-Alvarez Dec 17 2011 at 17:23
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 (1) I am pretty sure that the OP is hoping to improve something like the result in en.wikipedia.org/wiki/… (2) OP may wish to look up the very beautiful and extensive study of "quadrature formulas." This area deals with selecting appropriate points in order to best approximate given families of functions. It would be interesting to see if Chebyshev points give a better rate of approximation than uniformly distributed points. However, the result given on Wikipedia is so classical, I would strongly suggest a literature search first. – J.L. Nelson Dec 18 2011 at 7:16
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closed as not a real question by Mariano Suárez-Alvarez, Igor Rivin, Bill Johnson, Andres Caicedo, François G. Dorais♦ Dec 17 2011 at 17:35

1 Answer

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Can't understand your target or the motivation behind your question. Ofcourse, there are methods for approximating a continuous function, for example, by piecewise linear functions or you may just refer to some of the proofs of the Weierstrass approximation theorem. And make the question complete please.

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As we looking for a best approximation of continuous function uniformly, we know Bernstien polynomials as a proof to Weierstrass approximation Theorem is good theortical but bractically is not good. My question if we use Chebyshev points in Bernstien polynomials,does that give a better approximation , I tried but I still have problem ..... – nada Dec 18 2011 at 7:01
You can refer to: "Introduction to Numerical Analysis",Lecture-10,"Introduction to Splines",instructor-Prof. Amos Ron. – Somabha Mukherjee Dec 18 2011 at 15:39
If use Chebyshev points into Bernstien polynomials? – nada Dec 19 2011 at 5:50

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