Handy Polynomial Fitting with Bernstein Polynomials
11-10-2018, 10:22 PM
Post: #1
 Namir Senior Member Posts: 823 Joined: Dec 2013
Handy Polynomial Fitting with Bernstein Polynomials
Hi All,

I stumbled on an article discussing the advantages of using Bernstein polynomials for curve fitting. Unlike regular polynomials, the Bernstein polynomials offer smooth fitting with no wild deviations that occur when the order of the fitting classical polynomial is high.

The summary of Bernstein polynomials fitting of order n is:

1) map the values of the x observations to be in [0, 1] by using the minimum and maximum values of the original observations:

x = (x_orig - min(x_orig))/(max(x_orig) - min(x_orig))

2) Build the X matrix where the matrix elements are:

element(i,j) = combination(n,j-1) * x(i)^(j-1)*(1-x(i))^(n-j+1) for j=1 to n+1 and i=1 to number_of_observations

3) The last column of matrix X is filled with ones, needed to generate the constant term.
4) Solve X*c = y to obtain the regression coefficients c. The entities c and y are vectors.

I have tested the above concept using Excel and obtained satisfactory Bernstein polynomials fits.
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 Messages In This Thread Handy Polynomial Fitting with Bernstein Polynomials - Namir - 11-10-2018 10:22 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Valentin Albillo - 11-11-2018, 03:10 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Namir - 11-11-2018, 06:00 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-11-2018, 05:12 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-11-2018, 01:39 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Namir - 11-11-2018, 01:51 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-12-2018, 05:39 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Okken - 11-12-2018, 01:21 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-12-2018, 02:09 PM