Handy Polynomial Fitting with Bernstein Polynomials

11102018, 10:22 PM
Post: #1




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,j1) * x(i)^(j1)*(1x(i))^(nj+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. 

« Next Oldest  Next Newest »

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

User(s) browsing this thread: 1 Guest(s)