Handy Polynomial Fitting with Bernstein Polynomials

11112018, 05:12 AM
Post: #3




RE: Handy Polynomial Fitting with Bernstein Polynomials
(11112018 03:10 AM)Valentin Albillo Wrote: What values does produce your Bernstein fit for, say, order 2 ? The Bernstein Polynomial reproduces the function for \(f(x)=1\) and \(f(x)=x\): \( \begin{matrix} B_n(1;x)=1 \\ B_n(x;x)=x \end{matrix} \) However for \(f(x)=x^2\) we get: \( B_n(x^2;x) = x^2 + \frac{1}{n}x(1−x) \) Thus for \(n=10\) it's off by \(\frac{1}{40}\) at \(x=\frac{1}{2}\). While it can be shown that \(\lim _{n\to \infty }{B_{n}(f)}=f\) uniformly on the interval [0, 1] the convergence is rather slow. Cheers Thomas 

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Messages In This Thread 
Handy Polynomial Fitting with Bernstein Polynomials  Namir  11102018, 10:22 PM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Valentin Albillo  11112018, 03:10 AM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Namir  11112018, 06:00 AM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Thomas Klemm  11112018 05:12 AM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Thomas Klemm  11112018, 01:39 PM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Namir  11112018, 01:51 PM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Thomas Klemm  11122018, 05:39 AM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Thomas Okken  11122018, 01:21 PM
RE: Handy Polynomial Fitting with Bernstein Polynomials  Thomas Klemm  11122018, 02:09 PM

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